Robust model reference tracking control for high-order descriptor linear systems subject to parameter uncertainties

This paper investigates the robust model reference tracking control problem for high-order descriptor linear systems (HODLS) subject to norm-bounded parameter uncertainties. The problem is divided into two subproblems: a robust proportional plus derivative state feedback stabilization (RPPDSFS) problem and a robust feed-forward compensation (RFFC) problem. In the presence of uncertainties, by using the controller consisting of RPPDSFS part and RFFC part, all the signals of the closed-loop system are bounded. The latter is equivalent to seeking three coefficient matrices such that a series of linear matrix equations are satisfied, and simultaneously the effect caused by uncertainties is minimized. Based on the right coprime factorization, the RFFC problem is further converted into a minimization problem with a quadratic performance index and some linear constraints. Thereafter, a linear matrix equation that determines the optimal solution is achieved. The restrictive condition that the coefficient matrix of the augmented reference system is non-defective is relaxed, which reduces the conservativeness. A numerical example and the application of a three-axis dynamic flight motion simulator manifest the effectiveness and the practicability of the proposed algorithm.