H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function. Issue 13 (September 2019)

• Record Type: Journal Article
• Authors: Li, Panshuo; Li, Pengxu; Liu, Yun; Bao, Hong; Lu, Renquan
• Is Part Of: Journal of the Franklin Institute. Volume 356:Issue 13(2019)
• Page Start: 6968
• Page End: 6988
• Publication Date: 2019-09
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2019.06.008
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: In this paper, the H ∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H ∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H ∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.