Abstract: For a class of discrete-time linear switched systems with norm-bounded time-varying uncertainty, the problem of designing quadratic stabilizing state feedback controllers is investigated. The sufficient condition for existence of such controllers under arbitrary switching sequences is derived using multiple Lyapunov function technique. Furthermore, it is shown that this condition is equivalent to the solvability problem of a set of certain linear matrix inequalities (LMIs), which can be solved by the existing efficient convex optimization techniques. The solutions of the LMIs provide a parameterized representation of the quadratic stabilizing controllers. Finally, examples are given to illustrate the effectiveness of the proposed results.