LMI conditions for robust stability against parametric uncertainty: A behavioral approach

This paper is concerned with robust stability analysis against parametric uncertainty from the behavioral viewpoint. In the behavioral systems theory, quadratic differential forms (QDF´s) have been playing important roles in the studies of Lyapunov stability, dissipativity, LQ optimal control, etc. In this paper, we utilize QDF´s to derive new LMI conditions for robust stability of a linear system against parametric uncertainty both in the case where the system is described by the kernel representation and the state equation. The present LMI conditions guarantee the existence of a parameter-dependent Lyapunov function which allows less conservative robustness analysis, while the condition can be easily checked by convex optimization.