Robust linear controller design for discrete time systems with norm-bounded time-varying uncertainty

This paper is main concerned with the problem of robust stabilization of linear discrete-time systems with norm-bounded time-varying uncertainties. For such a problem, a simple method is presented whereby some sufficient conditions are derived so that discrete-time systems remain stable in the presence of norm-bounded time-varying uncertain perturbations. Some analytic method and a discrete type of Bellman-Gronwall inequality are employed to investigate such robust stability conditions. Moreover, in the light of such robust stability conditions, we can select the parameters of a dynamical controller so that uncertain discrete-time systems are stable, which lead to a controller design procedure. Finally, a numerical example is given to demonstrate the validity of results.