Stability Analysis of Discrete-Time Switched T-S Fuzzy Systems With All Subsystems Unstable

Liu, Can; Mao, Xiang; Xu, Xiaozeng; Zhang, Hongbin

doi:10.1109/access.2019.2911689

Cited by 4 publications

(7 citation statements)

References 33 publications

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“…Given a time interval

false[t_{0}, t false]

t \geq t_{0}

, we denote

N_{i} false(t, t_{0} false)

and

T_{i} false(t, t_{0} false)

as the switching number and total running time of the i th subsystem, respectively. Moreover, similar to the BMADT approach in [34–36], we also propose a divergence time

{\bar{T}}_{θ_{i}} false(t, t_{0} false) = \sum_{g = 0}^{k - 1} {\bar{T}}_{θ_{i}} false(t_{g + 1}, t_{g} false) + {\bar{T}}_{θ_{i}} false(t, t_{k} false),

where

{\bar{T}}_{θ_{i}} false(t, t_{g} false) = ({, \begin{aligned} 0, & t \leq t_{g} + θ_{i}, \\ t - t_{g} - θ_{i}, & t > t_{g} + θ_{i}, \end{aligned})

and

t \in false[t_{k}, t_{k + 1} false)

k \in double-struckN

i \in scriptF

θ_{i} \geq 0

is the compensation bound. Then, some definitions are introduced for further use.…”

Section: System Descriptions and Preliminariesmentioning

confidence: 99%

“…Besides, both the two ideas have been used simultaneously in [28, 29], while the corresponding shortcomings still exist. The case when all the subsystems are unstable is researched in [30–36]. In [34–37], a new bounded maximum ADT (BMADT) switching approach is introduced.…”

Section: Introductionmentioning

confidence: 99%

“…The case when all the subsystems are unstable is researched in [30–36]. In [34–37], a new bounded maximum ADT (BMADT) switching approach is introduced. Compared with the ADT, the BMADT is more general and can broaden the boundaries of the ADT.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the ADT, the BMADT is more general and can broaden the boundaries of the ADT. Whereas the BMADT in [34–37] are mode‐independent and have rooms for further improvement.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Unified stability criteria for continuous‐time switched T‐S fuzzy systems

Liu

Mao

Zheng

et al. 2020

IET Control Theory & Appl

Self Cite

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“…Given a time interval

false[t_{0}, t false]

t \geq t_{0}

, we denote

N_{i} false(t, t_{0} false)

and

T_{i} false(t, t_{0} false)

as the switching number and total running time of the i th subsystem, respectively. Moreover, similar to the BMADT approach in [34–36], we also propose a divergence time

{\bar{T}}_{θ_{i}} false(t, t_{0} false) = \sum_{g = 0}^{k - 1} {\bar{T}}_{θ_{i}} false(t_{g + 1}, t_{g} false) + {\bar{T}}_{θ_{i}} false(t, t_{k} false),

where

{\bar{T}}_{θ_{i}} false(t, t_{g} false) = ({, \begin{aligned} 0, & t \leq t_{g} + θ_{i}, \\ t - t_{g} - θ_{i}, & t > t_{g} + θ_{i}, \end{aligned})

and

t \in false[t_{k}, t_{k + 1} false)

k \in double-struckN

i \in scriptF

θ_{i} \geq 0

is the compensation bound. Then, some definitions are introduced for further use.…”

Section: System Descriptions and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Compared with the ADT, the BMADT is more general and can broaden the boundaries of the ADT. Whereas the BMADT in [34–37] are mode‐independent and have rooms for further improvement.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unified stability criteria for continuous‐time switched T‐S fuzzy systems

Liu

Mao

Zheng

et al. 2020

IET Control Theory & Appl

Self Cite

View full text Add to dashboard Cite

“…Therefore, the study of T-S fuzzy time-delay systems has become more and more popular in recent years. In particular, many significant and interesting results on stability analysis and the control synthesis of T-S fuzzy time-delay systems have been developed in the literature [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Ruan

Huang

2020

Symmetry

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This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi–Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov–Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

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RBFN-Based Adaptive Backstepping Sliding Mode Control of an Upper-Limb Exoskeleton With Dynamic Uncertainties

Chen

2019

IEEE Access

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In recent decades, robot-assisted rehabilitation therapy has been widely researched and proven to be effective in the motor function recovery of disabled individuals. In this paper, an adaptive backstepping sliding mode control approach combined with neural uncertainty observer is developed for upper-limb exoskeleton, which can help the human operator perform repetitive rehabilitation training. Firstly, a comprehensive overview about the therapeutic exoskeleton hardware and real-time control system is introduced. Then, the neural adaptive backstepping sliding mode controller (NABSMC) is developed based on radial basis function network (RBFN) to improve the trajectory tracking accuracy with external disturbances and dynamics errors. Next, the closed-loop stability of the proposed controller is demonstrated according to the Lyapunov stability theory. Finally, further experimental investigation are conducted on three volunteers to compare the control performance of NABSMC strategy with an optimal backstepping sliding mode control (OBSMC) strategy. The comparison results show that the proposed NABSMC algorithm is capable of achieving higher trajectory tracking accuracy and better step response characteristic during repetitive passive rehabilitation training. INDEX TERMS Upper-limb exoskeleton, rehabilitation training, adaptive backstepping sliding mode control, neural uncertainty observer, Lyapunov stability theory.

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Stability Analysis of Discrete-Time Switched T-S Fuzzy Systems With All Subsystems Unstable

Cited by 4 publications

References 33 publications

Unified stability criteria for continuous‐time switched T‐S fuzzy systems

Unified stability criteria for continuous‐time switched T‐S fuzzy systems

Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

RBFN-Based Adaptive Backstepping Sliding Mode Control of an Upper-Limb Exoskeleton With Dynamic Uncertainties

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