H∞ Guaranteed Cost Control for LPV Systems Subject to The Gain Constraint

• Published in: Asian journal of control Vol. 16; no. 2; pp. 609 - 616
• Main Authors: Zhao, Yangyang, Yang, Jianying, Lei, Zhengdong
• Format: Journal Article
• Language: English
• Published: Hoboken Blackwell Publishing Ltd 01.03.2014; Wiley Subscription Services, Inc
• Subjects: Closed loop systems; Feedback control systems; gain constraint; H∞ guaranteed cost control; LPV; Mathematical models; parameter-dependent Lyapunov function
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.681

This paper deals with the problem of H∞ guaranteed cost control for linear parameter varying (LPV) systems subject to the gain constraint. Specifically, our main goal is to design a controller such that the closed‐loop system is exponentially stable with the H∞ performance index, the quadratic performance index, and the gain within the desired constraints over the entire parameter region. In order to achieve this goal, less conservative and more practical sufficient conditions for the existence of the state feedback controller are proposed by introducing the parameter dependent Lyapunov function and many extra freedom degrees in terms of linear matrix inequalities and a free parameter matrix. The parameter matrix aspecially can regulate the gain freely without the influence of the desired performance to meet the additional design criteria enhancing the practicability and the design flexibility. As a special case, relevant results are extended to design a static output feedback controller. One numerical example is used to show advantages of the proposed approach.