State estimation for nonlinear switched systems under constrained switching

In this paper, the problem of state estimation for nonlinear discrete-time switched system is investigated. At first, the nonlinear switched system is represented as Takagi-Sugeno (T-S) fuzzy switched system, i.e., T-S fuzzy models are employed to approximate nonlinear parts. After that, a mode-dependent Luenberger-type observers under synchronous switching is employed to estimate the state of discrete-time T-S fuzzy switched system. By constructing multiply Lyapunov functions (MLFs) and common Lyapunov functions (CLFs), several sufficient conditions are established, in which the actual states of the estimated system under constrained switching (average dwell time (ADT) and mode-dependent average dwell time (MDADT) switching) and arbitrary switching can be tracked by the state of received observers, respectively. Finally, to testify the effectiveness of the proposed solution, one numerical example is provided.