Asymptotically Almost Automorphic Solutions To Nonautonomous Evolution Equations And Stability For Time-delayed Switched Systems

This paper investigates the existence of asymptotically almost automorphic milesolution to the following nonautonomous semilinear evolution equationsin a Banach space X, and the stability of the following weakly nonlinear time-delayedswitched systems in finite dimensional space RnIn Chapter 1, we introduce some concepts and basic properties of almost periodicfunctions,pseudo-almost periodic functions, almost automorphic functions, evolu-tion systems, Stepanov bounded functions, and time-delayed switched systems.In Chapter 2, we state our basic assumptions, such as {A(t)}t∈R satisfy theAcquistapace-Terreni'conditions. Moreover, three properties of almost automorphicfunctions and basic notations and properties of time-delayed switched systems are p-resented.In Chapter 3, we prove an existence theorem about asymptotically almost auto-morphic mild solution to the above nonautonomous semilinear evolution equation in aBanach space. Moreover, an example is given to illustrate the abstract result.Chapter 4 is about stability of weakly nonlinear time-delayed switched systems.We show a way to obtain a sufficient condition for ensuring exponential stability ofthe nonlinear switched systems by the multiple Lyapunov functions technique.