A LYAPUNOV ROBUSTNESS BOUND FOR LINEAR-SYSTEMS WITH PERIODIC UNCERTAINTIES

For linear systems involving uncertain parameters with known, constant nominal values and uncertain perturbations that vary sinusoidally with time, Lyapunov robustness anslysis is used to determine a stability bound, or margin, for the amplitudes of the parameter perturbations. This bound is the size of a hypercube in parameter space for which asymptotic stability is guaranteed. The bound, which is based on a quadratic Lyapunov function that depends linearly on parameter perturbations, varies with the frequency of the uncertain parameter perturbations. The bound is asymptotically proportional to the square root of this frequency as it becomes large.