Stabilization for a class of piecewise continuous-time switched control systems

Piecewise systems arise in many kinds of practical control systems due to the existence of certain effects, such as dead-zone, saturation, relays and hysteresis. This paper deals with the problem of exponential stabilization for a class of piecewise continuous-time switched control systems with nonlinear uncertainties, which are equivalent to the general form of piecewise switched affine nonlinear systems under the concept of linearization. Our approach hinges on the use of piecewise quadratic switched Lyapunov functions (PQSLFs). A stabilizing switching rule is presented when the corresponding PQSLFs exist. Conditions for exponential stabilization are presented in terms of linear matrix inequalities (LMIs). A robustly stabilizing state feedback controller can be constructed by using the feasible solution of the LMIs.