Robust stability of LTI discrete-time systems using sum-of-squares matrix polynomials

This paper deals with the robust stability of discrete-time systems with convex polytopic uncertainties. A necessary and sufficient condition for the robust stability of the system is presented, which states that the system is robust stable if and only if there exist three matrix polynomials to satisfy a specific relation. This existence condition can be easily converted to a semidefinite programming (SDP) problem, which can be solved using a number of available softwares