Filtering of Markovian Jump Delay Systems Based on a New Performance Index

Abstract-This paper investigates the finite-time eventtriggered H∞ control problem for Takagi-Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of the network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this work is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closedloop system is finite-time bounded and satisfies a prescribed H∞ performance level, but also the communication burden is reduced. Firstly, a sufficient condition is established for the finitetime bounded H∞ performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the desired controller design method is presented. Finally, two illustrative examples are given to explain the practicability and availability of the designed controller.

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“…Since ϕ ρi ρj , it could be obtained from (34) and (35) that for i < j, the following inequality holds:…”

Section: Resultsmentioning

confidence: 99%

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

Shen

Yan

et al. 2018

IEEE Trans. Fuzzy Syst.

417

120

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“…dϑds as a part of Lyapunov functional to derive delaydependent conditions, where the derivation of V 3 (t) was enlarged asV 3 …”

Section: θ-Dissipativity Resultsmentioning

confidence: 99%

“…(1) The dissipative theory gives a framework for the design and analysis of control systems using an input-output description based on energy-related considerations [3,4]. (2) The dissipative theory serves as a powerful or even indispensable tool in characterizing important system behaviors, such as stability and passivity, and has close connections with passivity theorem, bounded real lemma, Kalman-Yakubovich To name a few, by using a linear matrix inequality (LMI) approach, the problem of quadratic dissipative control for linear systems with or without uncertainty was studied in [6], where some necessary and sufficient conditions were presented for synthesis of feedback controllers to ensure the dissipativity of the resulting closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

Dissipativity and Invariant Sets for Neural Networks with Delay

Wang

Liu

Zheng

2015

Qualitative Analysis and Control of Complex Neural Networks With Delays

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Energy dissipation is a fundamental concept in dynamical systems. Passivity and dissipativity characterize the "energy" consumption of a dynamical system and form a powerful tool in many real applications. Passivity is closely related to stability and exhibits a compositional property for parallel and feedback interconnections. Passivity-based control is especially useful in the analysis of complex coupled systems. In Chap. 8, passivity problem is studied for a kind of neural networks with delays. Dissipativity and invariant sets are also the qualitative characteristics of a dynamical system. Such qualitative characteristics as passivity, dissipativity, and invariant sets are extensions and upgrades of the stability property, which can characterize the dynamics of dynamical systems more general. Based on such analysis, in this chapter some sufficient conditions for dissipativity and invariant sets have been established for a kind of RNNs with delay. The contents in this chapter are some extensions of the stability results of previous chapters. Delay-Dependent Dissipativity Conditionsfor Delayed RNNs IntroductionSince the study of dissipative systems was initiated by Willems [1], and further addressed by Hill and Moylan [2], there has been a steady increase in the interest of dissipative systems in the past several decades. The reasons are as follows:(1) The dissipative theory gives a framework for the design and analysis of control systems using an input-output description based on energy-related considerations [3,4]. (2) The dissipative theory serves as a powerful or even indispensable tool in characterizing important system behaviors, such as stability and passivity, and has close connections with passivity theorem, bounded real lemma, Kalman-Yakubovich To name a few, by using a linear matrix inequality (LMI) approach, the problem of quadratic dissipative control for linear systems with or without uncertainty was studied in [6], where some necessary and sufficient conditions were presented for synthesis of feedback controllers to ensure the dissipativity of the resulting closed-loop system. In [7], by proposing multiple storage functions and multiple supply rates, a framework of dissipativity theory for switched systems was established. More recently, some dissipativity conditions were presented in [8] for singular systems. When stochastic noise was taken into consideration in studying dissipative systems, the problems of sliding mode control were tackled in [9]. In [10], the robust reliable dissipative filtering problem has been investigated for uncertain discrete-time singular system with interval time-varying delays and sensor failures. The problem of static output-feedback dissipative control has been studied for linear continuous-time system based on an augmented system approach in [11]. A necessary and sufficient condition for the existence of a desired controller has been given, and a corresponding iterative algorithm has also been developed to solve the condition.On the other hand, as a special class of...

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“…In fact, we always get the upper and lower bound conditions such as (4). Conversely, when a time-varying delay s t ð Þ appears, it is usually assumed that _ s t ð Þ l < 1, which is too restricted [3,5,12]. In this article, we only require _ s t ð Þ l. Therefore, the condition of time-varying delay in this article is more general.…”

Section: Remarkmentioning

confidence: 99%

H_∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

et al. 2016

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This article investigates the problem of H 1 deconvolution filtering for a kind of uncertain descriptor hybrid system with state time-varying delays, limited communication capacity, and partially unknown transition rates. The limited communication capacity including signal transmission delays and data packet dropout. Mode-dependent and delay-dependent conditions are obtained by constructing a comprehensive stochastic Lyapunov-Krasovskii functional, which ensure the filtering error system is not only stochastically admissible but also satisfies a prescribed H 1 -norm level for all admissible uncertainties, signal transmission delays, and data packet dropout. The linear matrix inequalities technique is utilized to acquire the desired deconvolution filter parameters. An electrical RLC circuit example and two numerical examples are provided to demonstrate the usefulness and effectiveness of our methods.

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Filtering of Markovian Jump Delay Systems Based on a New Performance Index

Cited by 429 publications

References 44 publications

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

Dissipativity and Invariant Sets for Neural Networks with Delay

H_∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

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Filtering of Markovian Jump Delay Systems Based on a New Performance Index

Cited by 429 publications

References 44 publications

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

Dissipativity and Invariant Sets for Neural Networks with Delay

H∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

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H_∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates