Stability and stabilization of periodic piecewise linear systems: A matrix polynomial approach

Li, Panshuo; Lam, James; Kwok, Ka‐Wai; Lu, Renquan

doi:10.1016/j.automatica.2018.02.015

Cited by 81 publications

(58 citation statements)

References 23 publications

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“…But the system in [22] does not contain uncertainty and periodic systems were not considered in [22]. Li et al [23] proposed conditions of stability and stabilization for periodic piecewise linear systems but they neither considered discrete-time periodic systems nor taken uncertainty into consideration. Compared with [22,23], the results obtained in this paper have a greater range of applications.…”

Section: Corollarymentioning

confidence: 99%

Robust Stabilization of Discrete‐Time Switched Periodic Systems with Time Delays

et al. 2019

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This paper studies the problems of robust stability and robust stabilization for discrete-time switched periodic systems with time-varying delays and parameter uncertainty. We obtain the novel sufficient conditions to ensure the switched system is robustly asymptotically stable in terms of linear matrix inequalities. To obtain these conditions, we utilize a descriptor system method and introduce a switched Lyapunov-Krasovskii functional. The robust stability results are then extended to solve problems of robust stabilization via periodic state feedback. Novel sufficient conditions are established to ensure that the uncertain switched periodic system is robustly asymptotically stabilizable. Finally, we give two numerical examples to illustrate the effectiveness of our method.

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Section: Corollarymentioning

confidence: 99%

Robust Stabilization of Discrete‐Time Switched Periodic Systems with Time Delays

et al. 2019

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“…Besides its valuable theoretical properties, periodic piecewise system also has many applications in practice, including but not limited to power converters [5], and vibration systems [6]. Many results have been reported in [7][8][9], where the time-invariant subsystems are considered. However, the time-invariant subsystem formulations may render loss of some dynamic properties of the original system [10].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Non-Fragile Extended Dissipative Control of Periodic Piecewise Time-Varying Systems

Liu

Deng

et al. 2020

IEEE Access

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This paper studies the problem of finite-time non-fragile extended dissipative control for the periodic piecewise time-varying systems. First, based on the time-varying Lyapunov matrix and the matrix polynomial condition, a sufficient condition of finite-time boundedness for periodic piecewise time-varying subsystem is derived, and the finite-time extended dissipative performance is then analyzed. Furthermore, considering two types of time-varying controller perturbations, the non-fragile controllers are developed, which can guarantee the finite-time boundedness of periodic piecewise time-varying systems and satisfy the extended dissipative performance at the same time. Finally, numerical examples demonstrate the effectiveness of the proposed methods.

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“…Because of its value in application and continuous-time periodic systems study, the periodic piecewise system attracts much attention in recent years [9]- [15]. The stability, L 2 -gain and generalized H 2 performance indices are investigated in [9], [10], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…No matter the continuous or the multiple Lyapunov functions, the timevarying Lyapunov matrices established in the results mentioned above are formulated in the linear interpolation form of time. To further improve the Lyapunov matrix, the matrix polynomial formulation is proposed in [15], where more free variables are introduced in the constructed Lyapunov function. In that work, the constraints on exponential order of each subsystems are relaxed as well.…”

Section: Introductionmentioning

confidence: 99%

“…Nonconservative results are obtained for switched systems with guaranteed dwell time and arbitrary switching [26], [27]. These methods are also 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 L 2 -gain performance are proposed in this paper based on the matrix polynomial approach.…”

Section: Introductionmentioning

confidence: 99%

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

Xing

Liu

et al. 2020

IEEE Access

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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. INDEX TERMS Periodic piecewise systems, time-varying Lyapunov matrix, matrix polynomial, analysis synthesis.

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Stability and stabilization of periodic piecewise linear systems: A matrix polynomial approach

Cited by 81 publications

References 23 publications

Robust Stabilization of Discrete‐Time Switched Periodic Systems with Time Delays

Robust Stabilization of Discrete‐Time Switched Periodic Systems with Time Delays

Finite-Time Non-Fragile Extended Dissipative Control of Periodic Piecewise Time-Varying Systems

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

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