Feedback Stabilization Of Discrete-Time Singularly Perturbed Systems With Information Constraints

This paper considers the feedback stabilization of linear and nonlinear discrete time singularly perturbed systems under information constraints.In addition,we also consider the feedback stabilization of nonlinear singularly perturbed systems under limited communication channels with data packet dropout.Firstly,a proper encoder and decoder are given,so that the transmission error between the system state and the estimated state will converges to zero exponentially.At the same time,the appropriate channel capacity can also be obtained.Secondly,under the proper coder and decoder pairs,using Lyapunov theory and linear matrix inequality(LMI)methods,it is concluded that the resulting closed-loop system is input-to-state stable(ISS)with respect to the transmission error.Meanwhile,the asymptotically stable of the closed-loop system also can be guaranteed.In addition,the maximum packet loss rate is also obtained.Moreover,the maximum upper boundary of small perturbed parameters can also be obtained by generalized eigenvalue method(GEVP).Finally,using examples are given to verify the effectiveness of the methods.This paper mainly does the following works:1.When the discrete singularly perturbed systems are linear or non-linear,under the condition of limited communication channels,the uniform quantization method,Lyapunov theory,and linear matrix inequality method are used to obtained the transmission error of the systems converges to zero exponentially form by adding auxiliary system.In addition,a sufficient condition for the input-to-state stable of the system is obtained.2.In the case of a discrete singularly perturbed systems with nonlinear perturbed via a limited communication channel with data packet dropout,it is assumed that data packet dropout rates is subject to Bernoulli's random binomial distribution method.By using linear matrix inequality method and Lyapunov theory,it is concluded a sufficient condition that the system is asymptotic stability.