Robustness and stability margin of dynamical systems with structured uncertainties

In this paper, robustness and stability margin of linear or nonlinear systems are discussed. First, the robustness in linear or nonlinear dynamical systems with structured uncertainties is argued through the simultaneous Lyapunov inequalities. In order to find the common positive definite matrix P of the inequalities or to solve the so-called common Lyapunov problem, the P-region method proposed by the authors is roughly explained. Next, it is shown that the P-region corresponds to the robustness of systems, and the limit of the stability margin can be determined by the limit of the P-region. Also, as an example, the algebraic solution for the stability margin is compared with the numerical one.<>