This paper considers the stability analysis of linear continuous-time systems, and that the dynamic matrices are affected by uncertain time-varying parameters, which are assumed to be bounded, continuously differentiable, with bounded rates of variation. First, sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover, the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.
This paper deals with the robust stability of time-delay system with time-varying uncertainties via homogeneous polynomial Lyapunov-Krasovskii functions(HPLKF). We give a sufficient condition to demonstrate that the system is asymptotically stable.A new class of Lyapunov-Krasovskii function is introduced, whose main feature is that the conservativeness due to uncertainties is reduced. Numerical examples illustrate the effectiveness of our method.
