Robust stabilization of LPV systems with structured uncertainty using minimax controllers

This paper addresses a robust control scheduling scheme for uncertain linear parameter-varying systems with structured uncertainty. A gain-scheduled controller is proposed which employs a set of minimax optimal robust controllers and incorporates an interpolation rule to achieve continuity of the controller gain over a range of operating conditions. Novel weighted time-domain integral quadratic constraints are introduced to assist in the derivation of the controller. The key idea of the interpolation for the structured uncertainty case is to transform the parameterized algebraic Riccati inequalities into equivalent linear matrix inequalities. For every fixed value of the system parameter, the proposed controller guarantees robust stability and a certain bound on the worst-case performance of the corresponding uncertain closed loop system. Furthermore, a bound on the rate of parameter variations is obtained under which the closed loop LPV system is robustly stable. To obtain the proposed controller, a set of semi-definite programming problems are introduced; this enables an efficient numerical solution to the problem under consideration.