A new result on robust control for continuous-time systems with state-dependent polytopic uncertainties

In this paper, the problem of robust control for a class of continuous-time system with state-dependent polytopic uncertainties is investigated. The uncertainties of the underlying system are described by two state-dependent polytopic uncertain parameter vectors which are involved in the system state matrix and the control matrix, respectively. A non-quadratic Lyapunov function is used to reduce the conservatism of quadratic Lyapunov function approach, upon which the stability criterion is established and formulated via a set of bilinear matrix inequalities. Further, the existence conditions of a state-feedback controller is obtained such that the resulting closed-loop system is globally asymptotically stable. An example on the mass-spring-damper system is provided to illustrate the practical significance of the underlying uncertain system and the less conservatism of the developed theoretical results.