Continuous Time Switched Systems Robust The L <sub> 2 </ Sub>-l <sub> ¡Þ </ Sub> Control Problem Research

A switched system is a dynamical system that consists of a finite number of subsystems and a logical rule that orchestrates switching between these subsystems. 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. Based on these reasons, in the recent years, considerable attention has been drawn to the study of switched systems, which adopt the methods including convex combi-nation, single Lyapunov function, multiple Lyapunov function, piecewise Lyapunov function, common Lyapunov function, dwell time and average dwell time, and so on. Linear Matrix inequality (LMI) is an important analysis tool applicable to the study for switched systems. On the other hand, time delay is the inherent feature of many physical processes and a major source of instability and poor performance. Switched systems with time delay have a strong engineering background, such as in network control systems and power systems.This dissertation studies the problem of robust L2 - L∞control for continuous-time switched systems. More specifically, the main contributions are as follow:(1) Robust L2 - L∞control problem for linear uncertain time-varying switched system via controllability approach.Using controllability approach and LMIs, we give some sufficient conditions for this problem, which are described in terms of LMI and global null-controllability(GNC) of linear control systems. Meantime, the stabilizing feedback controllers can also be derived by solving a Riccati differential equations(RDE). Numerical example validates the correctness of the presented algorithms.2) The problem of robust L2 - L∞state feedback control for continuous-time time delays switched systems with parameter uncertainties.Based on free-weighting-matrix method, the problem of robust L2 - L∞state feedback control for continuous-time switched systems with parameter uncertainties and time de-lays was considered. 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 delays. A stabilizing switching controller can be derived by solving LMIs. To show the effectiveness and applicability of the proposed algorithms, a numerical example is provided.