Gain Scheduling Controller Synthesis with Spline-Type Parameter-Dependent Quadratic Forms via Dilated Linear Matrix Inequalities

This paper proposes a new synthesis of a gain scheduling controller based on the approximation of Lyapunov matrices by spline functions. The synthesis condition is described as dilated linear matrix inequalities which can be solved numerically. While in a previous study the derived feedback gains always have the same knots as the approximated Lyapunov matrices, our condition enables the feedback gains to have fewer knots without conservatism. Scheduled gains which are piecewise-linear on a parameter can also be obtained by adding constraints to the proposed synthesis condition.