Robust control of a class of LPV systems - a combined evolutionary - LMI approach

In this paper, recent analysis results on robust stability of linear parameter-varying (LPV) systems are used to develop a synthesis procedure for robust controller design that takes known bounds on the rate of parameter variation into account. This is achieved by first replacing robust stability conditions which take the form of linear matrix inequalities with an algebraic Riccati equation that is parameterized by a quadratic separator. The synthesis problem is then solved with a DK-iteration type of approach, where alternatingly the controller and the quadratic separator are fixed. In the K-step a combination of Riccati solver and evolutionary search is used to find the controller, and in the D-step an LMI problem is solved for the separator. An advantage of the new method is that dynamic order and structure of the controller (e.g. decentralized) can be freely chosen. A numerical design example is provided to illustrate the practicality and numerical efficiency of the proposed method