Stability margin evaluation for uncertain linear systems

A sufficient stability condition for parameter variation in a perturbed, continuous time, multivariable linear system, represented by a state space model is presented. Starting with the existence of an algebraic Riccati equation, a stability bound is derived from the polar decomposition of the nominal system matrix. Unlike previous work, the results are not dependent on the solution of the Lyapunov equation and, consequently, not a function of an arbitrarily selected positive definite matrix. In addition, the bound would appear to be the tightest possible, in that violation of the presented inequality can be shown to lead to instability. >