Quadratic separation for uncertain descriptor system analysis, strict LMI conditions

The past have witnessed the emergence of many techniques for solving parameter-dependent linear matrix inequality problems relative to robust analysis of dynamical systems. In these, a polynomial parameter-dependent structure of the Lyapunov function is chosen a priori for proving stability and conservative results are proposed to compute the coefficients of the matrix polynomial. Among such results some demonstrate that the polynomial structure of the Lyapunov function is related to an artificially augmented model in descriptor form. These contributions thus justify a renewed interest for robust analysis results in the descriptor context. Linear matrix inequality based formulas are proposed in the quadratic separation framework. Compared with previously derived results they have better numerical behavior, in particular because there is no need for equality constraints and most inequalities are strict.