Robust H∞ control for a class of switched nonlinear cascade systems via multiple Lyapunov functions approach

摘要

This paper addresses the problem of robust H∞ control for a class of switched nonlinear cascade systems with parameter uncertainty using the multiple Lyapunov functions (MLFs) approach. Each subsystem under consideration is composed of two cascade-connected parts. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton–Jacobi equations, sufficient conditions for the solvability of the robust H∞ control problem are presented. As an application, the hybrid robust H∞ control problem for a class of uncertain non-switched nonlinear cascade systems is solved when no single continuous controller is effective. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method.