Some Results On Stability Of Nonlinear Time-Varying Systems

LaSalle invariance principle is an effective tool in studying nonlinear time-invariant systems, However, this invariance principle can't be directly extended to nonlinear time-varying systems, becauseω-limit sets are not always invariant. In chapter 2, a modified detectability (weakly zero-state detectability)is employed to overcome the difficulty, then we propose a criterion by constructing a virtual output function. The criterion can be regarded as a generalization of LaSalle invariance principle in time-varying systems. In chapter 3 , we study the asymptotically almost periodic systems within the framework of limit systems by introducing the concept of conditional stability, and a general UAS theorem is proposed with a positive semi-definite Lyapunov function and its negative semi-definite time derivative. Finally, we show that the main theorem of chapter 2 is a necessary condition of the theorem of chapter 3.