Fixed-structure H_∞ controller design for systems with polytopic uncertainty: An LMI solution

This note provides a new method for fixed-structure H_∞ controller design for discrete-time single input single output (SISO) systems with polytopic uncertainty. New conditions are derived based on the concept of robust strict positive realness (SPRness) of an uncertain polynomial with respect to a parameter-dependent polynomial. The quality of this approximation depends on this SPR-maker. A procedure is proposed for choosing the parameter-dependent SPR-maker that guarantees the improvement of the performance for the designed controller in comparison with the traditional approaches employed fixed SPR-makers. The proposed conditions are given in terms of solutions to a set of linear matrix inequalities. The effectiveness of the proposed approach is demonstrated by comparing with the existing results.