Gain‐Scheduled<i>H</i>_<i>∞</i>Control for Tensor Product Type Polytopic Plants

Abstract A tensor product (TP) model transformation is a recently proposed technique for transforming a given linear parameter‐varying (LPV) model into polytopic model form, for which there are many methods that can be used for controller design. This paper proposes an alternative approach to the design of a gain‐scheduled output feedback H ∞ controller with guaranteed L 2 ‐gain parameter‐dependent performance for a class of TP type polytopic models using parameter‐dependent Lyapunov functions where the linear matrix inequalities (LMIs) need only to be evaluated at all vertices of the system state‐space model matrices and the variation rate of the scheduled parameters. In addition, a construction technique of the intermediate controller variables is also proposed as a matrix‐valued function in the polytopic coordinates of the scheduled parameters. The performance of the proposed approach is tested on a missile autopilot design problem. Furthermore, nonlinear simulation results show the effectiveness of these proposed techniques.