Article
Automation & Control Systems
Aysegul Kivilcim, Ozkan Karabacak, Rafael Wisniewski
Summary: Recent research has shown that almost global stability of nonlinear switched systems can be characterized using multiple Lyapunov densities. By discussing mode-dependent and edge-dependent average dwell times, the stability of the system is ensured.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2021)
Article
Automation & Control Systems
Shiyao Pan, Yuanfu Shao
Summary: This article discusses the exponential stability of totally positive switched linear systems (TPSLSs) for continuous-time and discrete-time cases. By employing the multiple piecewise-continuous linear copositive Lyapunov function (MPLCLF) and mode-dependent average dwell time (MDADT) methods, the article firstly considers TPSLSs containing both stable and unstable subsystems and proposes two kinds of switching strategies, which greatly reduce the conservativeness and provide more relaxed constraints on parameters compared with previous results. Two examples are given to illustrate the effectiveness of the results.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Automation & Control Systems
Qiang Yu, Guisheng Zhai
Summary: This paper introduces the concepts of Weighted Average Dwell Time (WADT) and Fast Weighted Average Dwell Time (FWADT) for continuous-time switched systems, and investigates their stability under a class of ergodic switching signals. The relationship between different ADT schemes and the WADT scheme is discussed, showing that classic schemes are included in the new one under certain conditions. The proposed switching law based on the (F)WADT scheme is more flexible and has a larger feasible region, and numerical examples are included to illustrate the validity and superiority of the developed techniques.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2021)
Article
Automation & Control Systems
Qiang Yu, Guisheng Zhai
Summary: A novel concept of L phi DADT is proposed in this paper along with new conditions for stability and stabilization of switched systems. These conditions can be easily calculated through simple linear matrix inequalities.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Article
Mathematics, Applied
Yaping Li, Xingwen Liu, Shiquan Shao, Jun Yang, Jun Wang
Summary: This paper addresses the stability issue of continuous-time switched linear systems with both stable and unstable subsystems, under switching signals that satisfy the constraint of mode-dependent average dwell time. A multiple discontinuous homogeneous polynomial Lyapunov function (MDHPLF) method is proposed, which provides less conservative conditions for guaranteeing exponential stability compared to existing works. It is proven that the conservatism of the stability condition reduces as the degree of MDHPLF increases. Furthermore, the results are applicable to scenarios where all subsystems are either stable or unstable.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Automation & Control Systems
Qian Wang, Haoyong Yu, Zheng-Guang Wu, Guoda Chen
Summary: This paper studies the stability analysis of input saturated discrete-time switched systems with average dwell-time based on the parametric discrete-time Riccati equation. State feedback and observer-based output feedback controllers are designed to ensure the exponential stability of the closed-loop system, with the advantage of being easily computed by solving the parametric discrete-time Lyapunov equation. The designed controllers exhibit good robustness to input saturation's structure uncertainty and the simulation results demonstrate the effectiveness of the proposed methods.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2021)
Article
Automation & Control Systems
Xiaoying Chen, Yang Liu, Bangxin Jiang, Jianquan Lu
Summary: This article investigates the exponential stability problem of switched systems with hybrid delayed impulses that depend on both current states and historical states. Some sufficient conditions for exponential stability based on Lyapunov functions are obtained. The stabilizing and destabilizing effects of time delays in impulses are also explored. The results show that delayed impulses may destabilize the system even when the continuous dynamics are stable. However, under certain conditions and with arbitrarily bounded impulsive intervals, the stability of the whole system cannot be destroyed by delayed impulses, and the sizes of the delays in the impulses can be theoretically arbitrarily finite. Finally, examples and simulations are provided to validate the derived results.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Weizhong Chen, Zhongyang Fei, Xudong Zhao, Michael V. Basin
Summary: This article aims to establish generic stability conditions for switched nonlinear systems with mode-dependent average dwell-time switching rules using Takagi-Sugeno fuzzy modeling. The proposed approach, called switching-signal-based multiple discontinuous Lyapunov function, can handle all unstable subsystems and provides less conservative bounds on the switching rules. The article also presents relaxed stability conditions for the system with both stable and unstable subsystems, as well as novel stability conditions for all stable and unstable subsystems.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Mathematics, Applied
Chao Ge, Chenlei Chang, Yajuan Liu, Chengyuan Liu
Summary: This article investigates the exponential synchronization problem for a class of switched coupled neural networks with mixed delays based on sampled-data control. By considering the mismatch between the controller and system, asynchronous switching occurs when switching signals appear in the sampling interval. Different from existing results, the switched neural networks are based on coupling information. An improved bilateral Lyapunov-Krasovskii functional is constructed, and sufficient conditions for the exponential stability of the synchronization error system are obtained using linear matrix inequalities through Bessel-Legendre inequality. The average dwell time is given in the form of an inequality that includes the maximum inter-event interval. Two examples are provided to demonstrate the validity and feasibility of the proposed method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Automation & Control Systems
Qiang Yu, Xiaoyan Yuan
Summary: By developing two novel switching schemes - the slow and fast weighted average dwell time, the stability problem for positive switched systems with subsystems stable or partially unstable is investigated. It can be seen that the new schemes cover both the average dwell time and mode-dependent average dwell time schemes under some mild conditions, and stability results based on our proposed approach have lower bound and are more flexible than the existing results. Three numerical examples comparing the relevant results are analyzed to illustrate the efficiency of the new findings.
Article
Computer Science, Information Systems
R. Vijay Aravind, P. Balasubramaniam
Summary: This paper addresses the exponential stabilization of switched interval type-2 fuzzy (IT-2F) time-delay systems using a non-fragile memory state feedback controller under an admissible edge-dependent average dwell time (AEDADT) scheme. It employs the concepts of slow switching and fast switching based on the AEDADT property to restrict stable and unstable modes. The globally uniformly exponential stability condition is ensured through the use of a non-fragile memory state feedback controller and the linear matrix inequalities (LMI) approach.
INFORMATION SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
R. Vadivel, S. Sabarathinam, Yongbao Wu, Kantapon Chaisena, Nallappan Gunasekaran
Summary: This study presents a T-S fuzzy-based sampled-data controller for switched chaotic systems. By designing a switched-based sampled-data fuzzy controller and proposing a novel time-dependent Lyapunov-Krasovskii functional approach, some sufficient conditions are established to achieve exponential stability of the proposed closed-loop system. The proposed approach has been demonstrated to be effective in the Lorenz system, Chen system, and Lu system.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Automation & Control Systems
Wenxiu Zhao, Yuangong Sun
Summary: This article addresses the absolute stability problem of switched Lurie systems by introducing two types of switched time-varying Lyapunov-Lurie functions and proposing sufficient conditions in terms of linear-matrix inequalities. The conservatism of the proposed method for absolute stability analysis is also studied, and numerical examples are provided to illustrate the given results.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Mathematics, Applied
Zi-Ming Wang, Xudong Zhao, Xiaodi Li, Airong Wei
Summary: In this paper, the authors discuss the finite-time boundedness (FTB) and H infinity control for a class of uncertain switched port-controlled Hamiltonian (PCH) systems via adaptive control strategies. They obtain sufficient conditions for FTB of uncertain switched PCH systems and derive conditions for finite-time H infinity control using a new MDADT scheme. The effectiveness of the proposed methods is illustrated through numerical simulations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Mengqian Liang, Yazhou Tian
Summary: This study addresses the practical stability problem of switched homogeneous positive nonlinear systems (SHPNS) and presents a new approach using the max-separable Lyapunov function (MSLF) to obtain sufficient conditions for practical stability. The obtained results are relatively concise, easily verifiable, and can be extended to a more general case.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
