Sliding-Mode Control for Fuzzy Stochastic Systems With Different Local-Input Matrices

Wang, Yingying; Zhang, Jian Yu; Zhang, Hua Guang

doi:10.1109/tsmc.2019.2944250

Cited by 4 publications

(5 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 4. It is noted that neither w(t) nor z(t) has changed between original system (Σ) in (1)-(3) and augmented system (Σ 1 ) in (10)- (12). Therefore, the robust passivity of system (Σ) is consistent with it of system (Σ 1 ) according to Definition 2.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 97%

“…Theorem 3. Consider system (Σ 1 ) in (10)- (12) with unavailable values of the bounds 1 , 2 , 3 , and . Suppose that sliding surface function is designed as (13) with K being determined by Remark 8 and G being chosen to make GB nonsingular.…”

Section: Adaptive Smc Law Synthesismentioning

confidence: 99%

“…According to Remarks 3 and 4, the admissibility and the robust passivity are not changed between the original system (Σ) in (1)-(3) and the augmented system (Σ 1 ) in (10)- (12). So we study the augmented system (Σ 1 ) for simplicity.…”

Section: Examplementioning

confidence: 99%

“…1,[4][5][6][7] In the past few decades, many researchers have focused on the research of singular systems and proposed many important results. These papers cover a variety of topics related to singular systems such as stability and stabilization problem, [8][9][10][11][12][13] dissipative control problem, [14][15][16] slow state variable feedback stabilization problem, 17 filtering problem, [18][19][20][21][22][23] dissipative fault-tolerant control problem based on slow state feedback, 24 and L 2 − L ∞ synchronization problem. 25 The research in this field is of great significance and challenge in theory and practice.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Liu

et al. 2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article addresses the passivity analysis and passification problems for a class of nonlinear singular time-varying delay systems with the special forms of uncertainties in both derivative matrix and some other system matrices by adopting adaptive sliding mode control (SMC) strategy. First, a distinctive state augmentation technique, which keeps the admissibility and the robust passivity unchanged, is employed due to "left-singular" form uncertainty in the derivative matrix (ie, E 0 (I + ΔE 0 ())). Next, an integral-type sliding surface, which involves the SMC gain matrix K, is constructed. By designing an appropriate Lyapunov-Krasovskii functional and introducing slack matrix approach, in which the slack matrixW is not constrained in contrast to most existing literatures, a new sufficient condition is derived to ensure that the resulting sliding mode dynamics is admissible and robustly passive for all admissible uncertainties. Additionally, for the passification problem, a delay-dependent sufficient condition is proposed in the form of strict linear matrix inequality (LMI), which not only removes the equality constraint but also makes the SMC gain matrix K solvable. Then a novel adaptive SMC law, which does not need to use the assumption that bounds of nonlinear perturbation function and external disturbance are known constants, is synthesized such that the finite-time reachability can be guaranteed. And the state information before and after state augmented transformation is utilized in SMC law design to help achieve better performance. Finally, four examples are presented to illustrate the effectiveness, superiority, and less conservativeness of the proposed scheme.

show abstract

Section: Problem Formulation and Preliminariesmentioning

confidence: 97%

Section: Adaptive Smc Law Synthesismentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Liu

et al. 2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…In 1999, Taniguchi et al combined the T-S fuzzy system with the singular system and promoted it to propose the T-S fuzzy singular system [24]. In recent years, various novel control techniques have been applied to the fuzzy singular system [25][26][27][28][29][30]. In many practical models, most of the systems are nonlinear and the nonlinearity of many nonlinear systems can be transformed into polynomials.…”

Section: Introductionmentioning

confidence: 99%

The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

Zhang

Jin

2021

Symmetry

View full text Add to dashboard Cite

In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.

show abstract

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

et al. 2022

View full text Add to dashboard Cite

Sliding-Mode Control for Fuzzy Stochastic Systems With Different Local-Input Matrices

Cited by 4 publications

References 36 publications

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

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

Contact Info

Product

Resources

About