The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating ...The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding ＂zeros＂ matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality （LMI）. LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.展开更多
In this paper the feasibility and stability of open-loop rain-max model predictive control （OL-MMMPC） for systems with additive bounded uncertainties are considered. It is found that the OL-MMMPC may be infeasible a...In this paper the feasibility and stability of open-loop rain-max model predictive control （OL-MMMPC） for systems with additive bounded uncertainties are considered. It is found that the OL-MMMPC may be infeasible and unstable if it is initially feasible. A sufficient condition for feasibility and stability of the OL- MMMPC is presented. Then an improved OL-MMMPC algorithm is proposed, which guarantees the robust stability of the closed-loop system once it is initially feasible. The effectiveness of this algorithm is illustrated by a simulation example.展开更多
A robust finite-horizon Kalman filter is designed for linear discrete-time systems subject to norm-bounded uncertainties in the modeling parameters and missing measurements.The missing measurements were described by a...A robust finite-horizon Kalman filter is designed for linear discrete-time systems subject to norm-bounded uncertainties in the modeling parameters and missing measurements.The missing measurements were described by a binary switching sequence satisfying a conditional probability distribution,the commonest cases in engineering,such that the expectation of the measurements could be utilized during the iteration process.To consider the uncertainties in the system model,an upperbound for the estimation error covariance was obtained since its real value was unaccessible.Our filter scheme is on the basis of minimizing the obtained upper bound where we refer to the deduction of a classic Kalman filter thus calculation of the derivatives are avoided.Simulations are presented to illustrate the effectiveness of the proposed approach.展开更多
This paper deals with the simultaneous estimation of states and unknown inputs for a class of Lipschitz nonlinear systems using only the measured outputs. The system is assumed to have bounded uncertainties that appea...This paper deals with the simultaneous estimation of states and unknown inputs for a class of Lipschitz nonlinear systems using only the measured outputs. The system is assumed to have bounded uncertainties that appear on both the state and output matrices. The observer design problem is formulated as a set of linear constraints which can be easily solved using linear matrix inequalities (LMI) technique. An application based on manipulator arm actuated by a direct current (DC) motor is presented to evaluate the performance of the proposed observer. The observer is applied to estimate both state and faults.展开更多
This paper presents a method of state estimation for uncertain nonlinear systems described by multiple models approach. The uncertainties, supposed as norm bounded type, are caused by some parameters＇ variations of t...This paper presents a method of state estimation for uncertain nonlinear systems described by multiple models approach. The uncertainties, supposed as norm bounded type, are caused by some parameters＇ variations of the nonlinear system. Linear matri~ inequalities （LMIs） have been established in order to ensure the stability conditions of the multiple observer which lead to determine the estimation gains. A sliding mode gain has been added in order to compensate the uncertainties. Numerical simulations through a state space model of a real process have been realized to show the robustness of the synthesized observer.展开更多
The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigat...The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H_∞ state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H_∞ performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.展开更多
The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii function...The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.展开更多
We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application...We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.展开更多
Minqing Xiao received the Ph.D.degree from Chongqing University,Chongqing,China,in 2008.He is currently a Professor with the College of Mathematics and Informatics,Fujian Normal University,Fuzhou,China.His current res...Minqing Xiao received the Ph.D.degree from Chongqing University,Chongqing,China,in 2008.He is currently a Professor with the College of Mathematics and Informatics,Fujian Normal University,Fuzhou,China.His current research interests include robust control/filter theory,delta operator systems,networked control systems,and switched systems;Guisheng Zhai received his B.S.degree from Fudan University,China,in 1988,and he received his M.E.and Ph.D.degrees,both in system science,from Kobe University,Japan,in 1993 and 1996,respectively.After two years of industrial experience,Dr.Zhai moved to Wakayama University,Japan,in 1998,and then to Osaka Prefecture University,Japan,in 2004.He held visiting professor positions at University of Notre Dame from August 2001 to July 2002,and at Purdue University from March 2016 through February 2017.In April 2010,he joined the faculty board of Shibaura Institute of Technology,Japan,where he currently is a full Professor of Mathematical Sciences.His research interests include large scale and decentralised control systems,robust control,switched systems and switching control,networked control and multi-agent systems,neural networks and signal processing,etc.Dr.Zhai is on the editorial board of several academic journals including IET Control Theory&Applications,International Journal of Applied Mathematics and Computer Science,Journal of Control and Decision,and Frontiers of Mechanical Engineering.He is a Senior Member of IEEE,a member of ISCIE,SICE,JSST and JSME.展开更多
This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping...This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.展开更多
基金Supported by the National Natural Science Foundation of China (60634020)the Natural Science Foundation of Hunan Province (06JJ50145)
文摘The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding ＂zeros＂ matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality （LMI）. LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.
文摘In this paper the feasibility and stability of open-loop rain-max model predictive control （OL-MMMPC） for systems with additive bounded uncertainties are considered. It is found that the OL-MMMPC may be infeasible and unstable if it is initially feasible. A sufficient condition for feasibility and stability of the OL- MMMPC is presented. Then an improved OL-MMMPC algorithm is proposed, which guarantees the robust stability of the closed-loop system once it is initially feasible. The effectiveness of this algorithm is illustrated by a simulation example.
基金Supported by the National Natural Science Foundation for Outstanding Youth(61422102)
文摘A robust finite-horizon Kalman filter is designed for linear discrete-time systems subject to norm-bounded uncertainties in the modeling parameters and missing measurements.The missing measurements were described by a binary switching sequence satisfying a conditional probability distribution,the commonest cases in engineering,such that the expectation of the measurements could be utilized during the iteration process.To consider the uncertainties in the system model,an upperbound for the estimation error covariance was obtained since its real value was unaccessible.Our filter scheme is on the basis of minimizing the obtained upper bound where we refer to the deduction of a classic Kalman filter thus calculation of the derivatives are avoided.Simulations are presented to illustrate the effectiveness of the proposed approach.
文摘This paper deals with the simultaneous estimation of states and unknown inputs for a class of Lipschitz nonlinear systems using only the measured outputs. The system is assumed to have bounded uncertainties that appear on both the state and output matrices. The observer design problem is formulated as a set of linear constraints which can be easily solved using linear matrix inequalities (LMI) technique. An application based on manipulator arm actuated by a direct current (DC) motor is presented to evaluate the performance of the proposed observer. The observer is applied to estimate both state and faults.
文摘This paper presents a method of state estimation for uncertain nonlinear systems described by multiple models approach. The uncertainties, supposed as norm bounded type, are caused by some parameters＇ variations of the nonlinear system. Linear matri~ inequalities （LMIs） have been established in order to ensure the stability conditions of the multiple observer which lead to determine the estimation gains. A sliding mode gain has been added in order to compensate the uncertainties. Numerical simulations through a state space model of a real process have been realized to show the robustness of the synthesized observer.
基金Project (60474003) supported by the National Natural Science Foundation of China project(20050533028) supported bythe Specialized Research Fund for the Doctoral Programof Higher Education of China
文摘The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H_∞ state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H_∞ performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.
文摘The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.
基金Supported by the DGRST Research Project LR11ES11CMCU Program 10G/1503
文摘We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.
基金This research has been supported in part by National Science Foundation of Fujian Province of China under Grant 2017J01567the Fundamental Research Funds for the Central Universities under grant no.JBK190502Japan Ministry of Education,Sciences and Culture under Grants-in-Aid for Scientific Research(C)21560471.
文摘Minqing Xiao received the Ph.D.degree from Chongqing University,Chongqing,China,in 2008.He is currently a Professor with the College of Mathematics and Informatics,Fujian Normal University,Fuzhou,China.His current research interests include robust control/filter theory,delta operator systems,networked control systems,and switched systems;Guisheng Zhai received his B.S.degree from Fudan University,China,in 1988,and he received his M.E.and Ph.D.degrees,both in system science,from Kobe University,Japan,in 1993 and 1996,respectively.After two years of industrial experience,Dr.Zhai moved to Wakayama University,Japan,in 1998,and then to Osaka Prefecture University,Japan,in 2004.He held visiting professor positions at University of Notre Dame from August 2001 to July 2002,and at Purdue University from March 2016 through February 2017.In April 2010,he joined the faculty board of Shibaura Institute of Technology,Japan,where he currently is a full Professor of Mathematical Sciences.His research interests include large scale and decentralised control systems,robust control,switched systems and switching control,networked control and multi-agent systems,neural networks and signal processing,etc.Dr.Zhai is on the editorial board of several academic journals including IET Control Theory&Applications,International Journal of Applied Mathematics and Computer Science,Journal of Control and Decision,and Frontiers of Mechanical Engineering.He is a Senior Member of IEEE,a member of ISCIE,SICE,JSST and JSME.
文摘This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.
