Stabilization of switched time-delay systems with only unstable subsystems: a new approach based on a vibration model of 1.5 degrees of freedom

Fu, Teng; Zhou, Yusheng

doi:10.1016/j.amc.2021.126740

Cited by 9 publications

(7 citation statements)

References 31 publications

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“…By combining (30)- (35) and applying Lemma 1, we easily obtain that if (18), ( 19), ( 21), (23) hold and considering that l is arbitrary, for t…”

Section: Gmsuas With H ∞ Performance Analysismentioning

confidence: 99%

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Event‐triggered fault detection filter design for networked switched systems with all subsystems unstable and cyber attacks

Zhang,

Liu,

Zhang

et al. 2023

Adaptive Control & Signal

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SummaryThis article focuses on the issue of event‐triggered fault detection filters (FDF) design for networked switched systems. Compared with the existing fault detection literature, this article investigates the situation that all subsystems are unstable, and considers that stochastic cyber attacks will disrupt fault detection. An event‐triggered mechanism (ETM) that excludes Zeno behavior naturally is designed to economize limited network resources. Then considering the ETM‐induced delay term, the dynamics of the initial system combined with the ETM, fault detection filters, and the effects of cyber attacks are formulated as a new augment switched delayed residual model. Based on the constructed multiple piecewise discretized Lyapunov–Krasovskii function (MPDLKF) and the mode‐dependent dwell time (MDDT) method, sufficient conditions are obtained to guarantee globally mean‐square uniformly asymptotically stability of the new augment system. Moreover, a co‐design method of ETM matrices and FDF gains is proposed. Finally, simulation results are provided to verify the feasibility and effectiveness of the proposed method.

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“…By combining (30)- (35) and applying Lemma 1, we easily obtain that if (18), ( 19), ( 21), (23) hold and considering that l is arbitrary, for t…”

Section: Gmsuas With H ∞ Performance Analysismentioning

confidence: 99%

“…However, this strategy does not apply to the case where all subsystems are unstable. In practical application, it is inevitable to encounter the NSSs with all modes unstable 23,24 . Hence, it has realistic necessity and theoretical value to further study the FDF design of NSSs when each subsystem is unstable.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered fault detection filter design for networked switched systems with all subsystems unstable and cyber attacks

Zhang,

Liu,

Zhang

et al. 2023

Adaptive Control & Signal

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“…In the recent decades, time-delay has become an active area of interest for the researchers due to its presence in several natural and physical systems like chemical processes, electrical circuits, power systems, control models, nuclear reactors, communication structures, and neural networks [15][16][17][18][19]. Time-delays have adverse effects on a system's performance and stability, as observed in [20]. Necessary and sufficient conditions for the delay-independent stability of linear time-invariant systems having single delay by using frequency discretization approach is presented in [21].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, static anti-windup scheme is proposed in [28] for the delayed nonlinear plants by employing reformulated Lipschitz condition and Wirtinger-based inequality; however, the results are applicable to a less general class of systems. Although, many aspects of time-delay systems have been addressed in the literature [15][16][17][18][19][20][21][22][23]; however, specifically, nonlinear timedelay systems with input saturation have not attained much research attention in the past decade. Therefore, further struggles are obligatory to explore new control and compensation schemes for nonlinear systems with input saturation and time-delay to address the aforementioned challenges.…”

Section: Introductionmentioning

confidence: 99%

Static anti-windup compensator design for locally Lipschitz systems under input and output delays

et al. 2023

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This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints.

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“…However, the above switching rules focus on the case of second‐order subsystems and cannot be directly applied to higher‐order switched systems. In fact, switched systems with higher‐order (

n\geqslant 3

) subsystems are inevitably encountered in many real modelings [33–35]. At present, relatively few studies have been conducted on the cases of third‐order or higher‐order unstable subsystems using state‐dependent switching laws, mainly because (i) the coupling between state components of subsystems is too complicated and (ii) the actual physical meaning of each subsystem is unclear, which results in difficulty of constructing energy function with weak conservativeness.…”

Section: Introductionmentioning

confidence: 99%

State‐dependent switching stabilization of third‐order switched linear systems consisting of two subsystems with fully positive real part characteristic roots

Yuan

Zhou

2023

Math Methods in App Sciences

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In the present work, we investigate the stability problem for a third‐order switched linear system in which the eigenvalues of each subsystem are all positive real parts. Firstly, we introduce a degenerated linear mechanical model with two state variables, in which one of the mechanical equations degenerates to a nonholonomic constraint, thereby such a mode being treated as a mechanical system with 1.5‐degrees of freedom (DOFs). Secondly, we establish the corresponding relationship between the mechanical system with 1.5‐DOFs and a standard third‐order linear system so as to define an energy function with actual physical meaning. Thirdly, an invertible transformation is introduced to convert a general third‐order linear system to a standard one so as to calculate energy function easily. On this basis, we reasonably introduce an intermediate subsystem for a general third‐order switched linear system with two unstable subsystems, such that each subsystem and the intermediate subsystem can be converted to standard third‐order linear systems simultaneously via an identical invertible transformation. Accordingly, we construct an energy ratio function with the help of the energy functions of the intermediate subsystem and two subsystems. Fourthly, based on the obtained energy ratio function, a proper state‐dependent switching law is designed to guarantee asymptotic stability of switched systems. That is, the energy loss from switching is large enough to offset the energy increased from unstable subsystems operation in a switching loop. Finally, simulation results demonstrate the effectiveness of the proposed state‐dependent switching approach.

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Stabilization of switched time-delay systems with only unstable subsystems: a new approach based on a vibration model of 1.5 degrees of freedom

Cited by 9 publications

References 31 publications

Event‐triggered fault detection filter design for networked switched systems with all subsystems unstable and cyber attacks

Event‐triggered fault detection filter design for networked switched systems with all subsystems unstable and cyber attacks

Static anti-windup compensator design for locally Lipschitz systems under input and output delays

State‐dependent switching stabilization of third‐order switched linear systems consisting of two subsystems with fully positive real part characteristic roots

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