Stabilization of delayed switched positive nonlinear systems under mode dependent average dwell time: A bumpless control scheme

Abstract

This study addresses a Bumpless Transfer (BT) stabilization for a class of switched positive nonlinear systems with time-varying delay. The nonlinear parts of the system are located in a sector of the positive orthant. The contribution of this study is to improve the transient performance of the switched positive systems by proposing a BT performance index at the switching instances and guaranteeing the L1–gain performance of the positive systems. A novel piecewise-continuous multiple Lyapunov–Krasovskii functional is utilized in the system’s stability analysis and control design. The control design methodology is established under Mode Dependent Average Dwell Time. Also, the BT stabilization of the system under asynchronous switching conditions is developed. Finally, a numerical example is provided to depict the effectiveness of the results.