Analysis and Synthesis of Robust Control Systems Using Linear Parameter Dependent Lyapunov Functions

This note provides sufficient robust stability conditions for continuous time polytopic systems. They are obtained from the Frobenius-Perron Theorem applied to the time derivative of a linear parameter dependent Lyapunov function and are expressed in terms of linear matrix inequalities (LMI). They contain as special cases, various sufficient stability conditions available in the literature to date. As a natural generalization, the determination of a guaranteed H₂ cost is addressed. A new gain parametrization is introduced in order to make possible the state feedback robust control synthesis using parameter dependent Lyapunov functions through linear matrix inequalities. Numerical examples are included for illustration