Observer-based finite-time $${H_\infty }$$ sliding mode control of stochastic nonlinear singular systems and its applications

Liu, Huawei; Zhao, Feng; Chen, Xiangyong; Hou, Huazhou; Qiu, Jianlong

doi:10.1007/s11071-022-07411-9

Cited by 15 publications

(8 citation statements)

References 35 publications

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“…To overcome the shortcomings of state feedback control, 33 observer-based control [34][35][36][37][38][39] and dynamic output feedback controllers 40 have been a hot topic. The dynamic output feedback controller can solve the stabilization problem when the states are completely unavailable.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the state observer is introduced to construct a controller. A large number of research results have emerged on the observer-based control problem, such as stabilization, 34 finite-time bounded, 35,39 event-triggered control. [36][37][38] These results estimated the full state information and the dimensionality of designed observers was consistent with the system.…”

Section: Introductionmentioning

confidence: 99%

“…By using improved lemma and the average dwell time (ADT) approach, some new sufficient conditions are given to ensure that the closed-loop augmented system is regular, impulse-free, has a unique solution and finite-time boundedness (FTB). Compared with full-order observer, [34][35][36][37][38] the reduced-order observer-based on controller has the advantages of lower dimension and lower physical realization cost. 2.…”

Section: Introductionmentioning

confidence: 99%

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Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

Shi,

Yang,

2024

Intl J Robust & Nonlinear

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SummaryThe reduced‐order observer‐based finite‐time control problem for one‐sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced‐order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse‐freeness, have a unique solution and finite‐time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced‐order observer‐based controller. Further, the lower finite‐time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

Shi,

Yang,

2024

Intl J Robust & Nonlinear

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“…Output feedback control and application for nonlinear system has been discussed in Reference 13. The method of sliding mode control for nonlinear singular systems has been proposed in Reference 14. Sliding mode control for nonlinear S‐MJSs has also been analyzed in Reference 15.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time composite control for fuzzy delayed semi‐Markovian jump systems with multiple disturbances and uncertainty

Zhu

et al. 2023

Adaptive Control & Signal

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Summary This article is concerned with the issue of finite‐time analysis for fuzzy semi‐Markovian jump systems (S‐MJSs) with multiple disturbances. Takagi–Sugeno fuzzy method is applied to address the nonlinear problem of closed‐loop systems. Unlike the existing research, delay, multiple disturbances, generally uncertain transition rate, uncertain parameters are all analyzed in a unify S‐MJSs framework. The aim of this study is to construct a composite control strategy for stable operation of S‐MJSs with multiple disturbances on the basis of the actual system requirements. For S‐MJSs, conservatism of analysis method and uncertainty of actual system are both the significant problems need to be solved urgently. First, the sufficient condition of S‐MJSs is obtained to guarantee the finite‐time stable performance through mathematical analysis and matrix inequality derivation. Second, disturbance observer based control and H∞$$ {H}_{\infty } $$ control are combined to deal with the effects of multiple disturbances which contain incomplete information disturbance and norm bounded disturbance. Third, fuzzy controller is designed to satisfy close‐loop systems finite‐time performance. Finally, the actual nonlinear example is presented to verify the accuracy of the approach.

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“…Such systems typically consist of differential equations and necessary algebraic constraints, which leads to a more general model framework. Hence, many attempts around the topic of singular systems have been given [6][7][8]. In the context of observer design for singular systems, a systematical Luenberger-like interval observer design approach was shown in [9].…”

Section: Introductionmentioning

confidence: 99%

Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

Cai

et al. 2022

Preprint

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This article makes some efforts towards discussing the problem of observer design for a kind of discrete-time T-S fuzzy singular systems corrupted by process disturbances and measurement noises. To situate our design scheme in a more practical context, the premise variables of fuzzy systems under consideration are unmeasurable, and the process disturbances are only partially decoupled rather than completely decoupled. By integrating the fuzzy Lyapunov function method and the linear matrix inequality technique, an unknown input observer which can not only decouple partial process disturbances, but also attenuate the influence of measurement noises and non-decoupled process disturbances is proposed to achieve state reconstruction. Particularly, to reduce the conservatism, some slack matrices and scalars are utilized in observer design to obtain extra degrees of freedom. Finally, the performance of theoretical results is fully verified via two numerical simulations.

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Observer-based finite-time $${H_\infty }$$ sliding mode control of stochastic nonlinear singular systems and its applications

Cited by 15 publications

References 35 publications

Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

Finite‐time composite control for fuzzy delayed semi‐Markovian jump systems with multiple disturbances and uncertainty

Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

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