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This paper investigates the problems of robust stability analysis and state feedback control design for discrete- time linear systems with time-varying parameters. It is assumed that the time-varying parameters lie inside a polytopic domain and have known bounds on their rate of variation. By exploiting geometric properties of the uncertainty domain, linear matrix inequality conditions that take into account the bounds on the rates of parameter variations are proposed. A feasible solution provides a parameter-dependent Lyapunov function assuring the robust stability of this class of systems. Extentions to deal with robust control design as well as gain-scheduling by state feedback are also provided in terms of linear matrix inequalities. Numerical examples illustrate the results.