Sequential Design of Switching $\mathscr{H}_{\infty}$ LPV State-Feedback Control

Abstract

This paper proposes a sequential approach for designing switching LPV (Linear Parameter-Varying) $\mathscr{H}_{\infty}$ state-feedback controllers with given division of scheduling parameter subregions. Different from the traditional simultaneous design of switching LPV control that usually results in a relatively high-dimensional optimization problem, the proposed method designs the switching LPV controllers sequentially, leading to a bundle of low-dimensional optimization problems to be solved iteratively. Interpolated controller variables are utilized on the overlapped subregions and independent PLMIs (Parametric Linear Matrix Inequalities) are formulated on individual subregion to synthesize switching LPV controllers. At the same time, the formulated PLMIs are able to guarantee that the $\mathscr{H}_{\infty}$ performances on overlapped subregions are no worse than adjacent subregions. With the proposed method, the $\mathscr{H}_{\infty}$ performance over the entire scheduling parameter region can be guaranteed by sequentially designing individual controller and interpolating controller variables on overlapped subregions. Application example shows the effectiveness of the proposed method and demonstrates improved performance over the conventional simultaneous design approach.