Multiple switching-time-dependent discretized Lyapunov functions/functionals methods for stability analysis of switched time-delay stochastic systems

Luo, Shixian; Deng, Fujin; Chen, Wu‐Hua

doi:10.1016/j.jfranklin.2017.12.005

Cited by 18 publications

(6 citation statements)

References 30 publications

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“…In view of the achievements of SSs and stochastic systems, the general stability and stabilization problems of time-varying delay switched stochastic systems (TVDSSSs) are researched. [15][16][17][18][19] Additionally, taking Reference 20 as an example, the exponential H ∞ filtering problems of TVDSSSs are discussed. In Reference 21, the problem of observer-based output tracking for TVDSSSs is studied.…”

Section: Introductionmentioning

confidence: 99%

H∞$$ {H}_{\infty } $$ tracking control for uncertain switched stochastic systems with mixed time‐varying delays

Deng

Zhang

Xia

et al. 2022

Intl J Robust & Nonlinear

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This article concerns the exponential H ∞ tracking control problem of uncertain switched stochastic systems with mixed time-varying delays including discrete delay and distributed delay. First, according to the multiple Lyapunov-Krasovskii functional described by the mixed time-varying delays and the average dwell time method, a delay-dependent sufficient conclusion is obtained, which makes the augmented system mean-square exponential stable and satisfies the H ∞ tracking performance. Then, the corresponding controllers are designed to ensure that the system has H ∞ model reference tracking performance based on the above stability analysis. Finally, a numerical example and water quality preservation problems are employed to corroborate the usefulness of the method. K E Y W O R D Saverage dwell time, H ∞ tracking control, mixed time-varying delays, uncertain switched stochastic system

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Section: Introductionmentioning

confidence: 99%

H∞$$ {H}_{\infty } $$ tracking control for uncertain switched stochastic systems with mixed time‐varying delays

Deng

Zhang

Xia

et al. 2022

Intl J Robust & Nonlinear

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“…A constructive adaptive control design for SS based on MLF was investigated by Long and Zhao (2014), where they were concerned with disturbance rejection problems of every subsystem and the overall system. Also, some researchers used MLF method with dwell time constraints to solve some control systhesis for SS. Luo et al (2018) analyzed the stability of switched stochastic systems with delays by introducing the piecewise switching-time-dependent discretized Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

Robust integral sliding mode control strategy under designed switching rules for uncertain switched linear systems via multiple Lyapunov functions

Zhang

2019

Transactions of the Institute of Measurement and Control

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This paper puts forward a switching rule stabilization design of the robust integral sliding mode control for uncertain switched systems. A kind of common robust integral sliding mode (CRISM) is firstly designed and the system matrices of subsystems under the sliding mode comprise a robust stable matrix set. The stability of the switched system (SS) under the sliding mode is then analyzed by multiple Lyapunov functions (MLF) method. Based on the presented design of CRISM, a sliding mode controller is devised so that the sliding mode can be reached. Finally, the correctness of the proposed method is verified through results of numerical and application simulations.

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“…Later, the work [22] extended the control method to stabilize deterministic p-norm nonlinear systems. Since stochastic factors widely exist in practice, stochastic systems play a significant role in modeling physical and engineering systems [23][24][25][26][27]. However, there are seldom results concentrating on the output feedback control problems for high-order switched stochastic nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Sampled‐data output feedback stabilization for a class of p‐norm switched stochastic nonlinear systems

Jiang

Zhai

2019

Asian Journal of Control

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This paper addresses the sampled-data output feedback stabilization problem for a class of p-norm switched stochastic nonlinear systems with uncontrollable and unobservable linearizations around the origin. With sampled measurements, a reduced-order observer is constructed to estimate the unmeasurable states. Based on adding a power integrator technique and the homogeneous domination approach, a sampled-data output feedback controller is designed. Subsequently, by choosing an appropriate Lyapunov-Krasoviskii functional combined with stochastic analysis techniques, it is shown that the closed-loop system is globally asymptotically stable in probability under the proposed controller with a proper sampling period. Finally, two examples are presented to illustrate the effectiveness of the proposed scheme.

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Multiple switching-time-dependent discretized Lyapunov functions/functionals methods for stability analysis of switched time-delay stochastic systems

Cited by 18 publications

References 30 publications

H∞$$ {H}_{\infty } $$ tracking control for uncertain switched stochastic systems with mixed time‐varying delays

H∞$$ {H}_{\infty } $$ tracking control for uncertain switched stochastic systems with mixed time‐varying delays

Robust integral sliding mode control strategy under designed switching rules for uncertain switched linear systems via multiple Lyapunov functions

Sampled‐data output feedback stabilization for a class of p‐norm switched stochastic nonlinear systems

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