Some Studies On Discrete-Time Singularly Perturbed Systems

Singularly perturbed systems contain a small parameter which leads the systems to order reduction and stiffness.Such systems possess two-time scale structure which makes the system more complicated.The singular perturbation model was first model to deal with these systems.In the past decades,it has been rapidly developed field of control system.Continuous and discrete-time singularly perturbed systems are of equal importance and many results exists for both.Based on the recent research on the topic of singularly perturbed system,this dissertation investigates some studies on discrete-time singularly perturbed systems and addresses some new results.To sum up,the major works in this dissertation are as follows:1.Firstly,the robust asymptotic stability for discrete-time singularly perturbed systems with disturbance is studied.By using the fixed-point principle and matrix inequality technique,sufficient conditions for the existence of the isolate root are presented. Furthermore,using two-time-scale decomposition technique,the robust asymptotic stability of the full-order system based on the corresponding slow and fast subsystems is obtained.2.Second paper investigates the robust stability and stabilization problem of discrete-time singularly perturbed systems,which are affected by disturbances and uncertainties.We first find a sufficient condition by using the fixed-point principle in terms of linear matrix inequalities(LMIs)in order to guarantee that the system is a standard singularly perturbed system.Slow subsystem(continuous-time)and fast subsystems(discrete-time)are obtained by decamping the original system.Then,the bases of two-time-scale decomposition technique,sufficient linear matrix inequalities(LMIs)condition is presented such that the original system is standard and input-to-state stable(ISS) simultaneously.Also,a state feedback controller is constructed by using the LMI approach such that the obtained closed-loop system is ISS.Lastly,a numerical example is given to validate the proposed approach.3.The problem of robust H? control of discrete-time singularly perturbed systems is addressed.We first find the fixed-point principle in linear matrix inequalities(LMIs) form to investigate the system to be standard.A sufficient condition is presented which guarantees that the given system is standard.Then,on the bases of decomposition technique a sufficient condition in form of LMIs is given such that the original system is asymptotically stable with a prescribed H? norm for small parameter.For the case where the nominal system is unstable or the desired H? performance cannot be achieved,the problem of designing a control law to make the resulting closed-loop system asymptotically stable with a desired H? performance is further addressed.Lastly,numerical examples are provided to validate the proposed method.