Observer-based Analysis And Control For Discrete-time Singularly Perturbed Systems

In this paper,the problem of H? observer-based analysis and control for discrete-time singularly perturbed systems has been considered.The main work is as follows:(1)The H? control problem for a class of discrete-time nonlinear systems with external disturbances is studied.Firstly,a method of full-order observer is provided,the concrete form of the observer is obtained by using Lyapunov method.Secondly,a state feedback control method based on the observer is presented,based on input-to-state stable(ISS)property and linear matrix inequality(LMI)technique,the specific form of state feedback controller for discrete-time nonlinear systems with external disturbances is derived.Meanwhile,criteria for stability of observer error system and closed-loop system with sufficient small disturbance attenuation level g are shown respectively,H? performance index is satisfied too.In addition,the methods of solving the upper bound of the perturbation parameters and the minimum of H? performance index are also provided.Finally,the example contrasts the conclusion of the chapter with the existing conclusion,the validity of the conclusion is verified by numerical simulation.(2)A new sliding surface is adopted to analyze the problem of H? sliding mode control for discrete-time singularly perturbed systems with uncertainties.Firstly,the chattering phenomenon in sliding mode control of discrete systems is reduced by observer method,the advanced techniques such as the method of Lyapunov and LMI are employed to derive a sufficient condition,which guarantee the observer error system in regard to estimated state with sufficient small disturbance attenuation level g is ISS,in this process,H? performance index is also satisfied.Next,according to the sliding mode control theory,a new stable sliding surface is designed and the corresponding control law is given.Based on ISS property,the criterion for the asymptotic stability of the sliding mode dynamics with respect to the observer error system is obtained,which guarantee the trajectories of the model can converge to the sliding surface s(k)=0 in a finite time interval.