Further results on delay-dependent state feedback H∞ control of linear parameter varying time-delay systems

• Published in: International journal of dynamics and control Vol. 10; no. 6; pp. 1847 - 1857
• Main Authors: Shahbazzadeh, Majid, Sadati, Seyed Jalil
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2022; Springer Nature B.V
• Subjects: Complexity; Control; Control and Systems Theory; Control systems design; Controllers; Design parameters; Dynamical Systems; Engineering; H-infinity control; Linear matrix inequalities; State feedback; Time delay systems; Vibration; Time-delay systems; Lyapunov-Krasovskii functional; performance; Linear matrix inequalities; State feedback controller; Linear parameter varying systems
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-022-00924-6

This paper is concerned with the H ∞ control problem for linear parameter varying time-delay systems subject to L 2 -norm bounded disturbances. Based on the Lyapunov-Krasovskii functional method, a new delay-dependent sufficient condition is derived for designing a state feedback H ∞ controller. In general, the coupling between decision variables and system matrices causes the results to be quite conservative. In order to obtain synthesis condition in terms of linear matrix inequalities, the well-known Young’s relation is employed to linearize the bilinear terms which unavoidably emerge in controller design for linear parameter varying time-delay systems. The proposed method can provide a controller with a larger delay range and a better disturbance attenuation effect. The efficiency and validity of the proposed control scheme are verified by the simulation results and comparisons.