A parametric multiple Lyapunov equations approach to switched systems with actuator saturation

This paper focuses on the problem of saturated control for switched systems with open-loop critical stable subsystems. A parametric multiple Lyapunov equations approach is developed for switched systems through eigen-structure assignment algorithm and parametric algebraic Riccati equations. Linear low-gain feedback controllers and a time-dependent switching law are designed to enforce asymptotic stability of the switched system with actuator saturation. A significant feature of the proposed controllers is that, for an arbitrarily large but bounded initial state, the actuator saturation can be avoided by decreasing the low-gain parameter. Moreover, the observer-based low-gain feedback controllers are derived if state measurements are unavailable. Two examples illustrate the effectiveness of the proposed approach at last.