Stability analysis and synthesis for slowly time varying systems based on non-common Lyapunov matrices

Recently, new stability analysis and controller synthesis methods based on non-common Lyapunov matrices are proposed. In this paper, we give another simple and easy proof for them using redundant descriptor form. Furthermore, we propose a sufficient condition for stability of slowly time-varying systems that have real rational uncertainties using the technique in the proof. The proposed condition is not more conservative than former methods and the quadratic stability.