A new LMI condition for the robust stability of linear time-varying systems

A new sufficient condition for the robust stability of linear systems with time-varying polytopic uncertainty is given in terms of linear matrix inequalities. The robust stability condition is assured by means of a parameter dependent Lyapunov function, taking into account bounds on the time derivatives of the uncertain parameters. Using line search, bounds on the magnitude as well as on the rates of change of the time-varying uncertain parameters can be determined solving a convex problem, encompassing quadratic stability results and providing less conservative evaluation than other similar methods from the literature. Moreover, constraints in the dynamic behavior of the uncertain parameters can be easily handled, providing a useful tool for the stability analysis of a class of nonideal switched systems.