Stability Analysis For Several Classes Of Linear Swiched Systems With Time-Delay

A switched system is an important class of hybrid dynamic systems, which is constituted by some continuous dynamic subsystems and discrete dynamic subsystems. It is well known that stability is an important nature of the systems. The methods used in the stability analysis for switched systems are extended to the linear switched systems with time-delay. So we can get more results.This paper is divided into the following sections:First of all, the researching background about the switched systems and the switched systems with time-delay is introduced. The methods used in the stability of the systems include: common Lyapunov function, single Lyapunov function, multiple Lyapunov functions, and common Lyapunov functional, single-Lyapunov functional, multiple-Lyapunov functional methods, and so on.Secondly, the stability of the linear switched systems with single time-delay is studied, and the systems are divided into two kinds of switched systems: independent and delay-dependent. The general methods are common Lyapunov functional, single-Lyapunov functional,and so on. A switching law is designed to find the conditions for asymptotic stability of the systems under the conditions of the matrix inequality. At the same time,corresponding numerical examples are given to verify the effectiveness of the theorem.Finally, the stability of the linear Switched Systems with Time-Delays is researched. The methods studied the stability of linear switched systems with single-delay are mainly extended to the switched systems with multiple delays and variable delays. The discussion also involves the definition of completeness, Riccati inequality and other knowledge.Last but not least, the paper is summaryed and the further researched is given for the switched systems with time-delay.