An exact stability analysis test for single-parameter polynomially-dependent linear systems

We provide a new condition for testing the stability of a single-parameter, polynomially-dependent linear system of polynomial degree N of the form x/spl dot/=A(/spl rho/)x, A(/spl rho/)=/spl Sigma//sub i=0//sup N//spl rho//sup i/ A/sub i/ (1) over a compact interval. The test is nonconservative and can be cast as a convex feasibility problem in terms of a pair of linear matrix inequalities (LMIs).