The Stability Analysis Of Linear Switched Delay Systems

In modern control theory, the switched systems are a typical class of hybridsystem. The factors that constituted the switched systems include a series of discrete orcontinuous subsystems and a switching signal, the switching signal control the runningorder and time of these subsystems. The composition of the switched systems areobviously different from common systems, which are consist of multiple subsystems,and the interaction between these systems makes the research of the stability of theswitched systems more complex and challenging than the general systems. Theaverage dwell time method combined exponential stability to determine the stability ofthe switching system in this paper.In the research of this paper take time delay which is a common and importantfactor into account, the main analysis of the stability of the switched systems with timedelay and feedback. Summarized as follows:Firstly, this paper researched the exponential stability of a class of continuouslinear time-varying delay switched systems. For the time-varying delay, assumed it hadan upper and a lower. Then divided into bounded differentiable and boundednondifferentiable, both of this cases were discussed. The Lyapunov stability theorem,LMI method and the average dwell time method are adopted in this paper. Only if thedwell time that stays in each stable subsystem within a long enough time, and canoffset more than a switch caused the system energy, the switching rules can ensure thatthe system is stable.Secondly, the exponential stability of switched linear systems with distributedtime-varying delay is researched. Time Delay in the control system can be subdividedinto Different types such as the neutral delay, distributed delay output delay. Switchingsystem with distributed time-varying delay, must constructing Lyapunov function indifferent forms. At the same time, this paper introduced free-weighting matrix methodand Newton-Leibniz formula, the last maintain stability criteria of the switcheddistributed time-varying delay systems by applicated the average dwell time.Finally, the stability results are extended to the delay-dependent stabilization design problem. A memoryless state feedback controller is set to the system,Constructing Lyapunov functions, introduced the LMI methods and the average dwelltime method, to obtain exponentially stable conditions the switched systems.