Local and Global Stabilization of Switched Linear Systems With Actuator Saturation

Utilizing the min-composite Lyapunov function and the min-projection switching strategy, we solve the local and global stabilization problems for switched linear systems by saturated, not necessarily stabilizing individually, linear feedback laws. Sufficient conditions are derived in the form of matrix inequalities under which the closed-loop system is locally asymptotically stable with an estimate of the domain of attraction or is globally asymptotically stable. The derived conditions are shown to be less conservative than the existing ones and, when used to guide the design of feedback laws, enable local stabilization with a larger estimate of the domain of attraction or global stabilization for a larger class of systems. Numerical examples illustrate the theoretical conclusions.