A NOTE ON QUADRATIC STABILITY OF UNCERTAIN LINEAR DISCRETE-TIME-SYSTEMS

In this paper we consider a linear discrete-time system depending on a vector of uncertain parameters, Assuming that the system matrix depen ds on parameters as the ratio of a multiaffine matrix-valued function and a multiaffine polynomial and that the parameters range in a hyper- rectangle, we show that the uncertain system is quadratically stable i f and only if the set of vertex systems is quadratically stable. This allows us to state a necessary and sufficient condition for quadratic stability in terms of the solvability of a feasibility problem involvi ng linear matrix inequalities (LMI's).