Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on ...Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on one hand,they have the most complete controllability theory.On the other hand,they can be nearly-controllable even if controllability fails.Firstly,controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived.Then,controllable canonical forms and nearly-controllable canonical forms of the systems are presented,respectively,where the corresponding transformation matrices are also explicitly constructed.Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61973014and 61573044。
文摘Controllable canonical forms play important roles in the analysis and design of control systems.In this paper,a fundamental class of discrete-time bilinear systems are considered.Such systems are of interest since,on one hand,they have the most complete controllability theory.On the other hand,they can be nearly-controllable even if controllability fails.Firstly,controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived.Then,controllable canonical forms and nearly-controllable canonical forms of the systems are presented,respectively,where the corresponding transformation matrices are also explicitly constructed.Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.
