Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Abstract

SummaryThis paper considers the global feedback exponential stabilization and L2 gain disturbance attenuation problems of the switched nonlinear polynomial systems with passive and nonpassive subsystems for any given average dwell time. In the existing result, it needs that there exists at least one open loop passive subsystem in the switched nonlinear system, which is unnecessary for the switched nonlinear polynomial system in this paper because the passivity of the subsystem can be obtained according to the passivity‐based feedback dissipative Hamiltonian realization. In addition, a parameterization of controller approach–based feedback exponential stabilization method of nonlinear polynomial system is described and utilized such that the Lyapunov function of the passive subsystem possesses the required decay rate to exponentially stabilize the switched nonlinear polynomial system. Comparing with the controller designed with the existing method, the obtained controller in this paper has much simpler structure and better performance. An example simulation is provided to illustrate the effectiveness of the proposed approach.