Exponential Stability Analysis For Several Classes Of Switched Delayed Systems

This dissertation deals with several classes of switched delayed systems includingimpulsive switched systems, switched descriptor systems, and sector-bounded nonlinearswitched descriptor systems. Based on Lyapunov functional approach and Razumikhintechnique, some exponential stability criteria are established. The main topics of this dis-sertation are consisted of the following aspects:1. The robust exponential stability of a class of uncertain nonlinear impulsiveswitched systems with delays is investigated. Firstly, the case of time-varying delays isconsidered. For such case, a novel type of piecewise Lyapunov functionals is constructedto derive the exponential stability. This type of functionals can efficiently overcome theimpulsive and switching jump of adjacent Lyapunov functionals at impulsive switchingtimes. Based on this, a delay-independent sufficient condition of exponential stabilityis presented by minimum dwell time. Secondly, for the case of switching delays, Weintroduce a novel type of piecewise Lyapunov–Razumikhin functions. Such functionsmay increase between impulsive switching instants. By Razumikhin technique, the delay-independent criteria of exponential stability are also established on the minimum dwelltime.2. The robust exponential admissibility of uncertain switched descriptor systemswith delays is studied. To prevent the switching impulsive phenomenon, an easily veri-fied condition is presented to check the switching-impulsive-free which ensures the con-sistence of algebraic equations. Base on this, we deal with two cases: time-varying delayand switching delay. For the former case, a novel type of piecewise Lyapunov functionalsis constructed to derive the uniform exponential admissibility. This type of functionalscan efficiently overcome the switching jump of adjacent Lyapunov functionals at switch-ing times. As a result, a delay-independent sufficient condition of uniform exponentialadmissibility is established on the minimum dwell time. For the latter case, by intro-ducing a novel type of piecewise Lyapunov functions which may decrease at switchingtimes, the delay-independent minimum dwell time criteria of robust exponential admissi-bility are also established. These criteria are naturally extended to the uncertain case.3. The problem of absolute exponential admissibility for a class of switched descrip- tor delayed systems with sector-bounded nonlinearity is focused. Under the regularityand impulsiveness-free, this problem, by a model transformation, is converted to the ex-ponential stability problem of differential subsystems and algebraic subsystems. Then theabsolute exponential admissibility criteria are established on the average dwell time byusing Lyapunov functional method and algebraic manipulation. Such criteria depend notonly on the delay range but also on the decay rate.