Observer-based fuzzy feedback control for nonlinear systems subject to transmission signal quantization

Chang, Xiao‐Heng; Jin, Xue

doi:10.1016/j.amc.2021.126657

Cited by 28 publications

(15 citation statements)

References 28 publications

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“…Note that Assumption 1 is the typical restriction commonly used in the design process of IOs. Besides, for a class of systems with the UBD uncertainties of the known non-identity structure 29,30…”

Section: Problem Statementmentioning

confidence: 99%

“…Therefore, when the matrix equation set (30) has a solution for the matrices M, V, and L, the rank condition rank…”

Section: R-io Solution and Optimizationmentioning

confidence: 99%

“…can be directly deduced from (30). Then, when pre-assigning L as rank [ C T L T ] T = n and F as a Metzler and Hurwitz matrix, the above equation set is further reduced into…”

Section: R-io Solution and Optimizationmentioning

confidence: 99%

“…Note that Assumption 1 is the typical restriction commonly used in the design process of IOs. Besides, for a class of systems with the UBD uncertainties of the known non‐identity structure 29,30

\begin{array}{ll}\dot{x}(t)& = Ax(t)+ Bu(t)+\mathbf{V}\upsilon (t),\\ {}y(t)& = Cx(t)+\mathbf{W}\omega (t),\end{array}

let

\tilde{\upsilon}(t)=\mathbf{V}\upsilon (t)

and

\tilde{\omega}(t)=\mathbf{W}\omega (t)

. By applying Assumption 1 and the inequality (1), we can directly transform (3) into the form (2) with

\overset{\overset{υ}{true}}{true} false(t false) = {boldV}^{+} \overset{υ}{true} false(t false) prefix- {boldV}^{prefix-} \underline{υ} false(t false), \underline{\overset{υ}{true}} false(t false) = {boldV}^{+} \underline{υ} false(t false) prefix- {boldV}^{prefix-} \overset{υ}{true} false(t false), \overset{\overset{ω}{true}}{true} false(t false) = {boldW}^{+} \overset{ω}{true}

…”

Section: Problem Statementmentioning

confidence: 99%

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Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Liu

Xie

Zhang

2022

Intl J Robust & Nonlinear

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This article investigates the reduced‐order interval observer (R‐IO) design technique for continuous‐time linear systems with unknown external disturbances and measurement noises. First, we propose a coupled R‐IO structure with more design degrees of freedom, and it can be directly applied not only to solve the difficulty of the error system cooperativity construction but to relax the constraint on the sensor measurement noises. Second, the R‐IO existence condition is derived as a set of matrix equations (MEs), and a complete solution, explicitly showing the available design parameters, to such an R‐IO is further obtained by solving the MEs. Third, using the solution, an integrated optimization indicator of the R‐IO performance is built as the valid selection mechanism of these parameters. Finally, the efficiency of the obtained results is illustrated through a numerical example and a practical example.

show abstract

Section: Problem Statementmentioning

confidence: 99%

“…Therefore, when the matrix equation set (30) has a solution for the matrices M, V, and L, the rank condition rank…”

Section: R-io Solution and Optimizationmentioning

confidence: 99%

“…can be directly deduced from (30). Then, when pre-assigning L as rank [ C T L T ] T = n and F as a Metzler and Hurwitz matrix, the above equation set is further reduced into…”

Section: R-io Solution and Optimizationmentioning

confidence: 99%

\begin{array}{ll}\dot{x}(t)& = Ax(t)+ Bu(t)+\mathbf{V}\upsilon (t),\\ {}y(t)& = Cx(t)+\mathbf{W}\omega (t),\end{array}

let

\tilde{\upsilon}(t)=\mathbf{V}\upsilon (t)

and

\tilde{\omega}(t)=\mathbf{W}\omega (t)

. By applying Assumption 1 and the inequality (1), we can directly transform (3) into the form (2) with

\overset{\overset{υ}{true}}{true} false(t false) = {boldV}^{+} \overset{υ}{true} false(t false) prefix- {boldV}^{prefix-} \underline{υ} false(t false), \underline{\overset{υ}{true}} false(t false) = {boldV}^{+} \underline{υ} false(t false) prefix- {boldV}^{prefix-} \overset{υ}{true} false(t false), \overset{\overset{ω}{true}}{true} false(t false) = {boldW}^{+} \overset{ω}{true}

…”

Section: Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Liu

Xie

Zhang

2022

Intl J Robust & Nonlinear

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show abstract

“…In addition, the control problem in Reference [30] is studied uncertain under actuated nonlinear switched systems with actuator faults using adaptive fuzzy hierarchical SMC. An observer-based Takagi-Sugeno (T-S) fuzzy model is considered in Reference [31], to formulate the quantized output for discrete-time nonlinear systems. A non-fragile H∞ filtering problem is considered for continuous time T-S fuzzy systems in Reference [32].…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Observer-Based Fault Detection in Continuous Time Linear Switched Systems

et al. 2022

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This paper studies the problem of fault detection for continuous time linear switched systems in the presence of disturbance. For this purpose, a fault detection sliding mode observer approach is designed to generate the residual signal. To minimize the effect of disturbance from the residual, the problem is formulated into H∞ filtering technique to increase more robustness. To deal with the issue of the switched systems stability, the Lyapunov-Krasovskii functional method is utilized along with average dwell time, and linear matrix inequalities are formulated to derive the sufficient conditions. The residual signal is evaluated, and an adaptive threshold is computed for both modes of the switched system. Finally, a simulation example for a case study of boost converter and a numerical example with both abrupt and incipient faults are illustrated to prove the efficacy of the proposed method.

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Parametric design of functional observer for second‐order linear time‐varying systems

Sun

Liu

2022

Asian Journal of Control

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This note constructs a functional observer for second‐order linear time‐varying (SOLTV) systems under framework of second‐order systems. Based on the assumption that the SOLTV system is observable, sufficient conditions for the existence of a second‐order functional observer are proposed. Combined with the solution of generalized Sylvester equation (GSE), the completely parameterized expressions of coefficient matrices of functional observer are proposed, which includes the free parameters representing degrees of freedom, and can be utilized to achieve some additional performance. Further, the design procedure is put forward, whose validity is verified through an example.

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Observer-based fuzzy feedback control for nonlinear systems subject to transmission signal quantization

Cited by 28 publications

References 28 publications

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Sliding Mode Observer-Based Fault Detection in Continuous Time Linear Switched Systems

Parametric design of functional observer for second‐order linear time‐varying systems

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