Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems

We present new algorithms for the robust stability analysis and gain-scheduled controller synthesis for linear systems affected by time-varying parametric uncertainties. Sufficient conditions for robust stability as well as conditions for the existence of a robustly stabilizing gain-scheduled controller are given in terms of a finite number of linear matrix inequalities; explicit formulae for constructing robustly stabilizing gain-scheduled controllers are given in terms of the feasible set of these LMI. Our approach is proven to be in general less conservative than existing methods for stability analysis and gain-scheduled controller synthesis for parameter-dependent linear systems; numerical examples are presented to show that our approach offers significant improvement in practice as well.