Non-fragile sliding mode observer based fault estimation for interval type-2 fuzzy singular fractional order systems

Zhang, Xuefeng; Zhang, Jin-Xi; Huang, Wenkai; Shi, Peng

doi:10.1080/00207721.2023.2177904

Cited by 8 publications

(7 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A unified criterion for admissibility without equality constraints and non-strictness is presented in Theorem 7, and is used to design a controller for an SFOS. Compared with the unified framework for stability in [19] and admissibility in [26,30], the proposed framework does not need to design the form of elements in linear matrix inequalities in different cases (1 ≤ α < 2 or 0 < α < 1) and is thus a truly unified framework. Strict linear matrix inequalities with few real variables are developed to test the stability and admissibility of the system.…”

Section: Discussionmentioning

confidence: 99%

“…Ref. [24] gave three different criteria for the admissibility and stabilization of SFOSs when the differential order is in the interval 0 < α < 1, which promoted the research [25,26] on related problems of SFOSs to some extent. The admissibility of SFOSs is still a hot topic in the field of control.…”

Section: Introductionmentioning

confidence: 99%

“…The criteria for the admissibility with differential order 1 ≤ α < 2 are given in [27], and the scheme for designing the controller is given in the form of bilinear matrix inequality. Based on the result in [19], the necessary and sufficient condition for admissibility and quadratic admissibility of SFOSs with fractional order 0 < α < 2 are given in [26,30], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…This means other related studies based on the premise of stability can only be divided into two cases, which makes the research results relatively fragmented. The stability and admissibility problems of FOSs with 0 < α < 2 have been studied in [26,30], but their results are still in the form of a piece-based function, that is, it is still divided into two criteria rather than a unified form. In view of the above observation, this paper is concerned with the stability and admissibility in terms of fractional order 0 < α < 2 and provides several unified frameworks, respectively, for stability and admissibility regardless of the fractional order interval.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalized Criteria for Admissibility of Singular Fractional Order Systems

Zhang

2023

Fractal Fract

Self Cite

View full text Add to dashboard Cite

Unified frameworks for fractional order systems with fractional order 0<α<2 are worth investigating. The aim of this paper is to provide a unified framework for stability and admissibility for fractional order systems and singular fractional order systems with 0<α<2, respectively. By virtue of the LMI region and GLMI region, five stability theorems are presented. Two admissibility theorems for singular fractional order systems are extended from Theorem 5, and, in particular, a strict LMI stability criterion involving the least real decision variables without equality constraint by isomorphic mapping and congruent transform. The equivalence between the admissibility Theorems 6 and 7 is derived. The proposed framework contains some other existing results in the case of 1≤α<2 or 0<α<1. Compared with published unified frameworks, the proposed framework is truly unified and does not require additional conditional assignment. Finally, without loss of generality, a unified control law is designed to make the singular feedback system admissible based on the criterion in a strict LMI framework and demonstrated by two numerical examples.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Criteria for Admissibility of Singular Fractional Order Systems

Zhang

2023

Fractal Fract

Self Cite

View full text Add to dashboard Cite

show abstract

“…Among them, fuzzy fault estimation using Takagi-Sugeno (T-S) fuzzy model [25] has the advantage of being able to easily achieve fault estimation for nonlinear systems [26]. Thus, many remarkable studies on fuzzy fault estimation are being presented as follows [27][28][29][30][31][32][33][34][35][36]: In [28,29], the continuous-and discrete-time fault estimation techniques have been presented for T-S fuzzy systems, respectively. In [27,[33][34][35], the various problems have been solved for the fuzzy fault estimation for IT2 fuzzy systems.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Fuzzy Fault Estimation Observer Design for Discrete-Time Nonlinear Interconnected Systems

Koo

2024

Electronics

View full text Add to dashboard Cite

In this paper, a fault estimation technique is proposed for discrete-time nonlinear interconnected systems with uncertain interconnections. To achieve the fault estimation, the decentralized fuzzy observer is adopted based on the Takagi–Sugeno fuzzy model. Based on the estimation error model with the subsystems of the interconnected system and its decentralized fuzzy observer, the fault estimation condition with H∞ performance is presented. The main idea of this paper is that a novel inequality condition for H∞ performance is used, and the sufficient condition is presented to guarantee the good fault estimation performance. Also, the decentralized fuzzy observer design condition for the fault estimation is converted into linear matrix inequality formats. Finally, a simulation example is provided, and the effectiveness of the proposed fault estimation technique is verified by comparison of the fault estimation performance.

show abstract