Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits

In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedback controller is then designed for the system. The effectiveness of the proposed approaches is illustrated by a numerical example, and the applicability of our theoretical findings is simultaneously demonstrated by modeling, analysis, and control design for a class of electronic circuits.