Switching controller for nonlinear systems: an invariant [K, KL] sector approach

This paper addresses the invariant [K, KL] sector as a special class of [K, KL] sector that holds the invariant characteristics with some appropriate control input, i.e. the energy of the system drastically decreases and state trajectory always remains inside the sector once it moves into it by the suitable control signal. The analysis of the nonlinear sector is regarded in comparison function prospective to outreach the property of uniformity. Here, the construction of [K, KL] sector and invariant [K, KL] sector relies on the selection of well-suited control-Lyapunov function. The switching control with invariant [K, KL] sector is designed to ensure the state trajectories move inside the nonlinear sector in finite-time and stay inside for all future time. Finally, the effectiveness of the proposed algorithm is illustrated with real physical examples.