Control synthesis via state feedback with finite frequency specifications for time-delay systems

Abstract

This article considers the problem of control synthesis via state feedback for linear time-delay systems with design specifications in finite frequency ranges. First, a finite frequency performance analysis condition for time-delay systems is presented. Then, a resulting state feedback control synthesis condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, the design procedure and the effectiveness of the proposed method are illustrated via a numerical design example.

Keywords:

• finite frequency specifications
• generalised Kalman–Yakubovic–Popov (GKYP) lemma
• linear matrix inequalities (LMIs)
• state feedback
• linear time-delay systems

Acknowledgements

This work was supported in part by Program for New Century Excellent Talents in University (NCET-04-0283), the Funds for Creative Research Groups of China (No. 60521003), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0421), the State Key Program of National Natural Science of China (Grant No. 60534010), the Funds of National Science of China (Grant No. 60674021) and the Funds of PhD Program of MOE, China (Grant No. 20060145019), the 111 Project (B08015).