New Conditions of Analysis and Synthesis for Periodic Piecewise Linear Systems With Matrix Polynomial Approach

Panshuo Li,Yun Liu,Mali Xing,Bin Zhang

doi:10.1109/access.2020.2980323

Panshuo Li, Yun Liu + Show 2 more

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Journal: IEEE Access	Publication Date: Jan 1, 2020
Citations: 8	License type: CC BY 4.0

Affiliation: Guangdong University of Technology

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In this paper, new conditions of the stability, stabilization and L 2 -gain performance of periodic piecewise systems are proposed. Both the continuous and discontinuous Lyapunov functions with dwell-time related time-varying Lyapunov matrix polynomial are adopted, and methods guaranteeing the positive and negative definiteness of a matrix polynomial are introduced. Exponential stability conditions are derived based on continuous and discontinuous Lyapunov functions, respectively. A stabilizing controller with time-varying controller gain is designed with continuous Lyapunov function and the weighted L 2 -gain performance based on the discontinuous Lyapunov matrix polynomial is studied as well. Numerical examples are used to verify the effectiveness of the proposed methods.

Highlights

The periodic system gives a framework for modeling systems with periodic features in engineering, ecological, and economic fields, such as rotor-blade systems [1], satellite attitude control systems [2], communication systems [3]
Periodic piecewise system is a special kind of periodic system because it consists of several subsystems in one period and the switching signal between subsystems is fixed and periodic
The weighted L2-gain performance analysis is carried out based on the discontinuous Lyapunov function with timevarying Lyapunov matrix polynomial, which has not been reported in previous works

Summary

INTRODUCTION

The periodic system gives a framework for modeling systems with periodic features in engineering, ecological, and economic fields, such as rotor-blade systems [1], satellite attitude control systems [2], communication systems [3]. Since control problems of continuoustime periodic systems are more challenging than the discretetime periodic systems [8], analysis and synthesis results of periodic piecewise systems can help study continuous-time periodic systems. P. Li et al.: New Conditions of Analysis and Synthesis for Periodic Piecewise Linear Systems matrix formats. Nonconservative results are obtained for switched systems with guaranteed dwell time and arbitrary switching [26], [27] These methods are adopted for periodic piecewise systems in [15] to handle the time-varying Lyapunov matrix polynomial. Motivated by the above works, new conditions of the stability, stabilizing and L2-gain performance are proposed in this paper based on the matrix polynomial approach. The continuous Lyapunov function could result in a directly solvable periodic time-varying controller. 2. The weighted L2-gain performance analysis is carried out based on the discontinuous Lyapunov function with timevarying Lyapunov matrix polynomial, which has not been reported in previous works.

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