Robust stabilization for discrete-time systems with slowly time-varying uncertainty

In this paper we construct a new class of parameter-dependent Lyapunov functions for discrete-time systems to guarantee robust stability in the presence of time-varying rate-restricted plant uncertainty. Extensions to a class of time-varying nonlinear uncertainty that generalizes the discrete-time multivariable Popov criterion are also considered. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of slowly time-varying real parameters.