We consider how small delays affect the integral-input-to-state stability(iss)property for a system.Our result is similar to the input-to-state stability(Iss)result obtained in[1]:the iss property will be preserved in...We consider how small delays affect the integral-input-to-state stability(iss)property for a system.Our result is similar to the input-to-state stability(Iss)result obtained in[1]:the iss property will be preserved in a practical and semi-global manner if the delay interval is small enough.However,since the iss quantifies the robust stability in terms of a generalized Li norm of the inputs instead of a generalized Loo norm of the inputs for the Iss case,the techniques and proofs for the Iss case do not apply to the iss case directly.While the proofs in[1]are based on the Lyapunov-Razumikhin approach,our proofs are based on the iss-Lyapunov functions for the zero-delay system.In addition to the interest by its own in showing how the iss property is affected by small delays,the result also serves to the study of the iss property for singularly perturbed systems.展开更多
文摘We consider how small delays affect the integral-input-to-state stability(iss)property for a system.Our result is similar to the input-to-state stability(Iss)result obtained in[1]:the iss property will be preserved in a practical and semi-global manner if the delay interval is small enough.However,since the iss quantifies the robust stability in terms of a generalized Li norm of the inputs instead of a generalized Loo norm of the inputs for the Iss case,the techniques and proofs for the Iss case do not apply to the iss case directly.While the proofs in[1]are based on the Lyapunov-Razumikhin approach,our proofs are based on the iss-Lyapunov functions for the zero-delay system.In addition to the interest by its own in showing how the iss property is affected by small delays,the result also serves to the study of the iss property for singularly perturbed systems.
