Robust <i>ℋ</i><sub>∞</sub> filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

Xu, Mingwei

doi:10.1177/1687814017745396

Cited by 3 publications

(3 citation statements)

References 36 publications

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“…Two cases have been considered in this study depending on whether the premise variables are measurable or unmeasurable. Moreover, the design of a robust

{H}_{\infty }

filtering for a class of T‐S fuzzy systems with time‐varying delay have been investigated in Reference 27. Based on a Lyapunov–Krasovskii functional in the delta domain, sufficient conditions ensuring the convergence of the filtering error were established in terms of LMIs in the case when the premise variables are known.…”

Section: Introductionmentioning

confidence: 99%

Design of asynchronous switched Takagi–Sugeno model‐based H_∞ filters with nonlinear consequent parts for switched nonlinear systems

Chekakta

Jabri

Motchon

et al. 2023

Adaptive Control & Signal

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Summary This paper investigates the design of asynchronous switched nonlinear H∞$$ {H}_{\infty } $$ filters for a class of continuous‐time nonlinear switched systems with mismatching switching laws and L2$$ {L}_2 $$ norm‐bounded disturbances. In this context, the switched nonlinear system is modelled as a switched Takagi–Sugeno (T‐S) model with nonlinear consequent parts, that is, where unmeasured nonlinear terms are kept in the nonlinear consequent parts in order to circumvent the occurrence of unmeasured premise variables, which is usually faced in conventional T‐S modeling without nonlinear consequent parts. In this framework, asynchronous switched T‐S filters with unmeasured nonlinear consequent parts are proposed to estimate unmeasured and/or disturbed system's outputs, even when the filter's switching law mismatches the switched nonlinear system's one, which can be in practice unknown or imprecisely measured. Based on a candidate multiple Lyapunov function, combined with a H∞$$ {H}_{\infty } $$ criterion, conditions are proposed in terms of Linear Matrix Inequalities for the design of the considered asynchronous switched T‐S filters with unmeasured nonlinear consequent parts. Compared with previous related works, these conditions have the advantage of being dwell‐time‐independent and less conservative, thanks to the incremental quadratic constraints employed to deal with the unmeasured nonlinear consequent parts. Furthermore, acknowledging that T‐S models are only representing nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error's domain of attraction is developed. Two illustrative examples are considered to validate the proposed results. An academic one is presented to illustrate the improvements brought in terms of conservatism by the proposed switched T‐S filter design methodology with regards to previous related studies. Then, a case study illustrates the effectiveness of this proposal from a switched nonlinear mass‐spring system inspired from related literature.

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“…Two cases have been considered in this study depending on whether the premise variables are measurable or unmeasurable. Moreover, the design of a robust

{H}_{\infty }

Section: Introductionmentioning

confidence: 99%

Design of asynchronous switched Takagi–Sugeno model‐based H_∞ filters with nonlinear consequent parts for switched nonlinear systems

Chekakta

Jabri

Motchon

et al. 2023

Adaptive Control & Signal

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“…For example, the problem of asymptotic stability and stabilization of delta operator systems with uncertainties and time-varying delays was studied in [9]. In Reference [10], the authors used the delta operator approach to investigates the robust H ∞ filtering design for T-Sfuzzy systems with uncertainties and time-varying delay. In Reference [11], the robust stability of delta operator systems was discussed via the three-term approximation approach.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

2019

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The design of an anti-windup controller for delta operator systems with time-varying delay and actuator saturation is addressed. By utilizing the input-output approach and three-term approximation, we first transform the original system into two equivalent interconnected subsystems. Then, by employing the scaled small-gain theorem, the Lyapunov–Krasovskii functional, and Wirtinger’s integral inequality, sufficient conditions for the synthesis of an anti-windup compensator are presented in the form of linear matrix inequalities (LMIs). The estimated domain of attraction is maximized by an optimization algorithm. Numerical examples are studied to show the merits of the proposed technique.

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“…The final paper in this group, by Xu, 18 applies the HN filtering design for Takagi-Sugeno fuzzy systems with time-varying delays and parameter uncertainties using the delta operator approach. The time-varying delays and parameter uncertainties are supposed to be of an internal-like type and a structured linear fractional form, respectively.…”

mentioning

confidence: 99%

Modeling, optimization, and control for complex networked systems

Zhu

Zhong

Karimi

et al. 2018

Advances in Mechanical Engineering

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Over the last decade, a succession of various complex systems has emerged in the field of automatic control, following the rapid development of information and communication technologies, such as manufacturing and production systems, robotics, spacecraft, smart grids, and intelligent transportation. The development of network technology brings many challenges for the modeling, control, and optimization of today's complex systems, as well as their engineering applications. In recent years, some preliminary results have emerged on complex systems in network environments, ranging from academic research to industrial applications, including Antsaklis and Baillieul, 1 Zhang et al., 2 Zhang et al., 3 Zhu et al.,4 Hespanha et al., 5 Gupta and Chow. 6 More and more researchers are working on addressing various analysis and synthesis issues simultaneously, compensating for the deficiencies associated with this medium. Therefore, the main purpose of this special collection is to brief researchers on both the theory and practice of advances in modeling, optimization, and control for complex dynamic systems in network environments, especially on those developments that have been made in the field of engineering, and mechanical engineering in particular.This special collection consists of 12 papers, all of which cover, but are not limited to, the proposed topics and can be divided into three groups. The first group mainly focuses on the issues of modeling and simulation analysis for mechanical systems in network environments, while the second addresses the issue of advanced control in complex networked systems. Finally, the third group is concerned with stability analysis and optimization for complex networked systems.In the first group, the paper by Tian et al. 7 presents an omnidirectional mobile platform with six mecanum wheels, positing that an omnidirectional mobile platform with six mecanum wheels is more flexible and can reach the desired position more easily in narrow workspaces. The kinematic model for this platform is constructed and verified using four kinds of motion state in the simulation. The motion features of the platform corresponding to the cases of six and four wheels are discussed, and the authors demonstrate the advantages of the platform with six wheels. Moreover, thanks to

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Robust ℋ_∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

Cited by 3 publications

References 36 publications

Design of asynchronous switched Takagi–Sugeno model‐based H_∞ filters with nonlinear consequent parts for switched nonlinear systems

Design of asynchronous switched Takagi–Sugeno model‐based H_∞ filters with nonlinear consequent parts for switched nonlinear systems

Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

Modeling, optimization, and control for complex networked systems

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Robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

Cited by 3 publications

References 36 publications

Design of asynchronous switched Takagi–Sugeno model‐based H∞ filters with nonlinear consequent parts for switched nonlinear systems

Design of asynchronous switched Takagi–Sugeno model‐based H∞ filters with nonlinear consequent parts for switched nonlinear systems

Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

Modeling, optimization, and control for complex networked systems

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Robust ℋ_∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

Design of asynchronous switched Takagi–Sugeno model‐based H_∞ filters with nonlinear consequent parts for switched nonlinear systems

Design of asynchronous switched Takagi–Sugeno model‐based H_∞ filters with nonlinear consequent parts for switched nonlinear systems