Robust stability analysis for a class of uncertain discrete-time linear systems

In this paper, A necessary and sufficient condition of robust normal and quadratic stability (RNQS) is derived for uncertain discrete-time linear systems. The parameter uncertainties are assumed to be time-invariant norm-bounded appearing not only in the state matrix but also in difference matrix. The condition is expressed in terms of a set of linear matrix inequalities (LMIs). It enables us to determine robust stability of uncertain systems easily by solving some LMIs. The quadratic stability condition for a state space system is a special case of the proposed condition. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.