Exponential stability analysis of discrete-time almost periodic piecewise nonlinear systems

This paper focuses on exponential stability analysis for discrete-time almost periodic piecewise nonlinear systems (APPNSs) with uncertain dwell time of subsystems. A discrete-time APPNS has a fundamental period, during which a finite number of subsystems that constitute the system are cyclically activated. Such systems can be modeled as switched systems with cyclically switching signals. With the assumption that the vector field of each subsystem of discrete-time APPNSs is continuously differentiable, a Lyapunov theorem is presented first to verify the exponential stability of discrete-time APPNSs. Then, a linearization method is employed and a mixed-mode time-varying homogeneous Lyapunov function is constructed to derive specific stability conditions expressed by linear matrix inequalities (LMIs). Note that this condition can verify the exponential stability of the considered nonlinear systems, as well as that of the corresponding linearized systems. Furthermore, the linearization method used here can be applied to general switched systems.