Reliable observer-based H∞ control for discrete-time fuzzy systems with time-varying delays and stochastic actuator faults via scaled small gain theorem

Wang, Shenquan; Jiang, Yulian; Li, Yuanchun; Liu, Derong

doi:10.1016/j.neucom.2014.06.069

Cited by 28 publications

(15 citation statements)

References 34 publications

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“…Based on the work of Wang et al, we obtain

x ((), k + 1) = A ((), θ) x ((), k) + \frac{1}{2} A_{d} ((), θ) ([], x ((), k - d_{1}) + x ((), k - d_{2}) + d_{12} w_{d} ((), k)) + B ((), θ) u ((), k),

where 1/2[ x ( k − d 1 ) + x ( k − d 2 )] is regarded as the approximation of x ( k − d ( k )), and d 12 /2 w d ( k ) is the approximation error with d 12 = d 2 − d 1 and

w_{d} ((), k) = \frac{2}{d_{12}} ({}, x ((), k - d ((), k)) - \frac{1}{2} ([], x ((), k - d_{1}) + x ((), k - d_{2}))) .

Employ the first‐order forward difference operator as

normalΔ x ((), k) = x ((), k + 1) - x ((), k) .

By and , we obtain

\begin{matrix} lefttrue \\ w_{d} (k) = \frac{2}{d_{12}} \{x (k - d (k)) - \frac{1}{2} [x (k - d_{1}) + x (k - d_{2})]\} \\ = \frac{1}{d_{12}} \{[x (k - d (k)) - x (k - d_{1})]\} \end{matrix}

…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

“…We perform the congruent transformation on Θ( θ ): premultiplying an invertible symmetric matrix diag{ P ( θ ) −1 , P ( θ ) −1 , P ( θ ) −1 , S −1 , I } and, meanwhile, postmultiplying the transposition of this matrix, then denoting X ( θ ) = P ( θ ) −1 ,

\overset{S}{true} = S^{- 1}

{\overset{true‾}{R}}_{l} ((), θ) = X {(θ)}^{T} R_{l} ((), θ) X ((), θ)

, and

{\overset{true‾}{Q}}_{l} ((), θ) = X {(θ)}^{T} Q_{l} ((), θ) X ((), θ)

, ( l = 1, 2), we have

([], \begin{array}{c} {\overset{true^}{normalΞ}}_{1} ((), θ) & ([], \begin{array}{c} {\overset{true^}{normalΞ}}_{2} {(θ)}^{T} & d_{1} {\overset{true^}{normalΞ}}_{3} {(θ)}^{T} & d_{2} {\overset{true^}{normalΞ}}_{3} {(θ)}^{T} & {\overset{true^}{normalΞ}}_{3} {(θ)}^{T} & {\overset{Ξ}{true}}_{4}^{T} \end{array}) \\ * & normalΨ ((), θ) \end{array}) < 0 .

Obviously, the nonlinear terms still exist in . From the work of Wang et al, we have

\begin{matrix} lefttrue \\ - R_{l} {((), θ)}^{- 1} = - X {((), θ)}^{T} (X {((), θ)}^{- T} R_{l} {((), θ)}^{- 1} X {((), θ)}^{- 1}) X (θ) \leq - X {((), θ)}^{T} - X () \end{matrix}

…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

See 1 more Smart Citation

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Yuan

2019

Intl J Robust & Nonlinear

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Summary This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.

show abstract

“…Based on the work of Wang et al, we obtain

x ((), k + 1) = A ((), θ) x ((), k) + \frac{1}{2} A_{d} ((), θ) ([], x ((), k - d_{1}) + x ((), k - d_{2}) + d_{12} w_{d} ((), k)) + B ((), θ) u ((), k),

where 1/2[ x ( k − d 1 ) + x ( k − d 2 )] is regarded as the approximation of x ( k − d ( k )), and d 12 /2 w d ( k ) is the approximation error with d 12 = d 2 − d 1 and

w_{d} ((), k) = \frac{2}{d_{12}} ({}, x ((), k - d ((), k)) - \frac{1}{2} ([], x ((), k - d_{1}) + x ((), k - d_{2}))) .

Employ the first‐order forward difference operator as

normalΔ x ((), k) = x ((), k + 1) - x ((), k) .

By and , we obtain

\begin{matrix} lefttrue \\ w_{d} (k) = \frac{2}{d_{12}} \{x (k - d (k)) - \frac{1}{2} [x (k - d_{1}) + x (k - d_{2})]\} \\ = \frac{1}{d_{12}} \{[x (k - d (k)) - x (k - d_{1})]\} \end{matrix}

…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

\overset{S}{true} = S^{- 1}

{\overset{true‾}{R}}_{l} ((), θ) = X {(θ)}^{T} R_{l} ((), θ) X ((), θ)

, and

{\overset{true‾}{Q}}_{l} ((), θ) = X {(θ)}^{T} Q_{l} ((), θ) X ((), θ)

, ( l = 1, 2), we have

([], \begin{array}{c} {\overset{true^}{normalΞ}}_{1} ((), θ) & ([], \begin{array}{c} {\overset{true^}{normalΞ}}_{2} {(θ)}^{T} & d_{1} {\overset{true^}{normalΞ}}_{3} {(θ)}^{T} & d_{2} {\overset{true^}{normalΞ}}_{3} {(θ)}^{T} & {\overset{true^}{normalΞ}}_{3} {(θ)}^{T} & {\overset{Ξ}{true}}_{4}^{T} \end{array}) \\ * & normalΨ ((), θ) \end{array}) < 0 .

Obviously, the nonlinear terms still exist in . From the work of Wang et al, we have

\begin{matrix} lefttrue \\ - R_{l} {((), θ)}^{- 1} = - X {((), θ)}^{T} (X {((), θ)}^{- T} R_{l} {((), θ)}^{- 1} X {((), θ)}^{- 1}) X (θ) \leq - X {((), θ)}^{T} - X () \end{matrix}

…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Yuan

2019

Intl J Robust & Nonlinear

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show abstract

“…Through applying the LPV system and GS control scheme, the standard control theories for time‐invarying systems can be applied to stability analysis of linear‐time varying systems. Therefore, much control schemes have been developed, including H 2 / H ∞ performance control, 8‐10 observer control, 11‐13 adaptive control, 13,14 fault estimation, 15 sampled data control, 16 and predictive control 17 . Unfortunately, only few works were proposed to discuss the pole‐assignment issues for improving the transient response of the LPV systems.…”

Section: Introductionmentioning

confidence: 99%

Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Chang

Yen

et al. 2020

Optim Control Appl Methods

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Summary This paper addresses a pole‐assignment control problem for discrete‐time linear parameter varying (LPV) systems. Based on LPV modeling approach, time‐varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain‐scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole‐assignment constraint. Moreover, two cases of Lyapunov function are respectively employed to derive some sufficient conditions which belong to linear matrix inequality (LMI) problems. Solving those derived conditions, the corresponding GS scheduled controller can be designed such that the asymptotical stability and pole assignment of LPV systems are guaranteed. Finally, a controller problem of truck‐trailer system is used to demonstrate the applicability and effectiveness of the proposed design methods.

show abstract

“…For instance, robust sliding mode control of the uncertain semi-Markovian jump system was researched in [17]. An observer was established for the fuzzy system containing stochastic actuator faults in [18]. is paper will further study the stability of the semi-Markovian jump networked control system with actuator faults and delays.…”

Section: Introductionmentioning

confidence: 99%

Event‐Triggered Stability Analysis of Semi‐Markovian Jump Networked Control System with Actuator Faults and Time‐Varying Delay via Bessel–Legendre Inequalities

Guo

et al. 2019

Complexity

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This paper discusses the stability of semi-Markovian jump networked control system containing time-varying delay and actuator faults. The system dynamic is optimized while the network resource is saved by introducing an improved static event-triggered mechanism. For deriving a less conservative stability criterion, the Bessel–Legendre inequalities approach is employed to the stability analysis and plays a major role. By constructing the enhanced Lyapunov–Krasovskii functional (LKF) relevant to the Legendre polynomials, a stability criterion with lower conservativeness indexed by N is derived, and the conservativeness will decrease as N increases. In addition, a controller is designed. To prove the validity of this paper, numerical examples are provided at the last.

show abstract

Reliable observer-based H∞ control for discrete-time fuzzy systems with time-varying delays and stochastic actuator faults via scaled small gain theorem

Cited by 28 publications

References 34 publications

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Event‐Triggered Stability Analysis of Semi‐Markovian Jump Networked Control System with Actuator Faults and Time‐Varying Delay via Bessel–Legendre Inequalities

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