Robustness analysis and gain-scheduled controller synthesis for rational parameter-dependent systems using parameter-dependent Lyapunov functions

For linear systems with a rational dependence on some unknown but measurable time-varying parameters, we use parameter-dependent Lyapunov functions to devise algorithms for robust stability analysis and gain-scheduled controller synthesis. A sufficient condition for the existence of a parameter-dependent Lyapunov function that proves robust stability is given in terms of a finite number of linear matrix inequalities. This sufficient condition is then used to solve the gain-scheduled stabilizing controller synthesis problem