Varying Delay Discrete Time Switched Systems Robust <sub> 2 </ Sub>-l <sub> ¡Þ </ Sub> Research,

Switched system is an important hybrid dynamical system consisting of subsystems and a switching rule that specifies the switching among them.Many real-world processes and systems can be modeled as switched system,such as mechanical systems,the automotive industry,aircraft and air traffic control,switching power converts,and many other fields.In view of its so many applications in practical fields,during the last decades,switched system has been attracting much attention of researchers.So far,there have been many studies on stability analysis and design for switched systems,which adopt the methods including convex combination,single Lyapunov function,multiple Lyapunov function,piecewise Lyapunov function,common Lyapunov function,dwell time and average dwell time,and so on.Linear Matrix Ineauality(LMI) is an important analysis tool applicable to the study for switched systems.This thesis mainly focuses on the problem of robust l₂-l_∞performance analysis for discrete-time switched systems with parameter uncertainties and time-varying delays. More specifically,the main contributions are as follows:1) The problem of robust l₂-l_∞filter for discrete-time switched systems with parameter uncertainties and time-varying delays.Based on the descriptor system method,the problem of robust l₂-l_∞filtering for uncerrain discrete-time switched system with time-varying delays.The parameter uncertainties are assumed to be time-varying but norm-bounded.The purpose is to design a filtering, which guarantees that the error system is asymptotically stable and satisfies the prescribed scale for all admissible uncertainties.Delay-dependent conditions for the solvability of the problem are developed.A l₂-l_∞filtering can also be derived by solving a set of LMIs. Simulation validates the correctness of the presented algorithm.2) The problem of robust l₂-l_∞guaranteed cost filter for discrete-time switched systems with parameter uncertainties and time-varying delays.Based on linear matrix inequality and a finite sum inequality,the problem of robust l₂-l_∞guaranteed cost filtering for uncertain discrete-time switched system with time-varying delays.The parameter uncertainties are assumed to be time-varying but norm-bounded. The purpose is to design a stable guaranteed cost filtering,which guarantees that the error system is asymptotically stable and the cost function Value is not more than a specified upper bound for all admissible uncertainties.Delay-dependent conditions for the solvability of the problem are developed.A l₂-l_∞guaranteed cost filtering can also be derived by solving a set of LMIs,which can be efficiently handled by using standard numerical algorithms.3) The problem of robust l₂-l_∞state feedback control for discrete-time switched systems with parameter uncertainties and interval-like time delays.Based on the descriptor systems and free-weighting-matrix method,the problem of robust l₂-l_∞state feedback control for discrete-time switched systems with parameter uncertainties and mode-dependent interval-like time delays was considered.The parameter uncertainties are assumed to be time-varying but norm-bounded.The purpose is to construct a switched state feedback controller such that the resulting closed-loop system is asymptotically stable while satisfying a prescribed l₂-l_∞performance level irrespective of the parameter uncertainties and time-varying delays.By transforming the given switched systems to an equivalent descriptor form,delay-dependent conditions for the solvability of the problem are developed,and a stabilizing switching controller can be derived.A numerical example is provided to show the effectiveness and applicability of the proposed algorithms.