Delay-dependent generalized H2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

Li, Jiangrong; Li, Junmin; Xia, Zhile

doi:10.2478/v10006-011-0046-6

Cited by 10 publications

(6 citation statements)

References 31 publications

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“…proof: To investigate the stability problem of the system (9), we construct the following piecewise quadratic Lypunov functional (PQLF) candidates: (18) whereP i ,Q, i = 1, 2, · · · , s are symmetric positive-definite matrices.…”

Section: Resultsmentioning

confidence: 99%

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Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

2013

2013 9th Asian Control Conference (ASCC)

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This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays. Based on the piecewise quadratic Lyapunov functional (PQLF), the fuzzy observer-based controllers are designed for T-S fuzzy bilinear stochastic systems. It is shown that the stability in the mean square for discrete T-S fuzzy bilinear stochastic systems can be established if there exists a set of PQLF which can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities(LMIs) constraints. An iterative algorithm makes use of sequential linear programming matrix method (SLPMM) to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.

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Section: Resultsmentioning

confidence: 99%

“…Based on CQLF and make the gain K is known, the paper of [16] studied the robust H ∞ fuzzy linear observer for a discrete fuzzy bilinear systems. Based on PQLF, the observer-based fuzzy controller for fuzzy bilinear model has been studied in [17][18].…”

Section: Introductionmentioning

confidence: 99%

Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

2013

2013 9th Asian Control Conference (ASCC)

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“…A piecewise static-output-feedback controller and a piecewise Lyapunov function were designed to make the uncertain closed-loop fuzzy system stochastically stable with guaranteed performance (Qiu et al, 2010). The works of Su et al (2013;2014), Qiu et al (2009) and Li et al (2011) discussed T-S fuzzy systems with time delay. Although there have been many successful applications for the discrete T-S fuzzy linear system, this model for approximation of nonlinear systems still has its structural limitations.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems

Duan

Zhang

et al. 2016

International Journal of Applied Mathematics and Computer Science

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This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the "soft" constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T-S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T-S fuzzy hyperbolic model with the discrete T-S fuzzy linear one are also given to illustrate the advantage of our approach.

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“…T-S fuzzy stochastic systems with state time-vary or distributed delays were studied in Refs. [35][36][37][38][39]. The researches of fractional order T-S fuzzy systems on robust stability, stability analysis about "0<α <1", and decentralized stabilization in multiple time delays were presented in Refs.…”

Section: Introductionmentioning

confidence: 99%

Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

Li¹,

Li²,

Duan³

2017

Modern Fuzzy Control Systems and Its Applications

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This paper focuses on the non-fragile guaranteed cost control problem for a class of TakagiSugeno (T-S) fuzzy time-varying delay systems with local bilinear models and different state and input delays. A non-fragile guaranteed cost state-feedback controller is designed such that the closed-loop T-S fuzzy local bilinear control system is delay-dependent asymptotically stable, and the closed-loop fuzzy system performance is constrained to a certain upper bound when the additive controller gain perturbations exist. By employing the linear matrix inequality (LMI) technique, sufficient conditions are established for the existence of desired non-fragile guaranteed cost controllers. The simulation examples show that the proposed approach is effective and feasible.Keywords: fuzzy control, non-fragile guaranteed cost control, delay-dependent, linear matrix inequality (LMI), T-S fuzzy bilinear model IntroductionIn recent years, T-S (Takagi-Sugeno) model-based fuzzy control has attracted wide attention, essentially because the fuzzy model is an effective and flexible tool for the control of nonlinear systems [1][2][3][4][5][6][7][8]. Through the application of sector nonlinearity approach, local approximation in fuzzy partition spaces or other different approximation methods, T-S fuzzy models will be used to approximate or exactly represent a nonlinear system in a compact set of state variables. The merit of the model is that the consequent part of a fuzzy rule is a linear dynamic subsystem, which makes it possible to apply the classical and mature linear systems theory to nonlinear systems. Further, by using the fuzzy inference method, the overall fuzzy model will © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. be obtained. A fuzzy controller is designed via the method titled 'parallel distributed compensation (PDC) ' [3-6], the main idea of which is that for each linear subsystem, the corresponding linear controller is carried out. Finally, the overall nonlinear controller is obtained via fuzzy blending of each individual linear controller. Based on the above content, T-S fuzzy model has been widely studied, and many results have been obtained [1][2][3][4][5][6][7][8]. In practical applications, time delay often occurs in many dynamic systems such as biological systems, network systems, etc. It is shown that the existence of delays usually becomes the source of instability and deteriorating performance of systems [3][4][5][6][7][8]. In general, when delay-dependent results were calculated, the emergence of the inner product between two vectors often makes the process of calculation more complicated. In order to avoid it, some model transformations were utilized in many papers, unfortunately, which will arouse the generation of an inequality, resulting in possible conse...

show abstract

Delay-dependent generalized H2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

Cited by 10 publications

References 31 publications

Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems

Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

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Delay-dependent generalized H2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

Cited by 10 publications

References 31 publications

Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays

Stability analysis and H∞ control of discrete T–S fuzzy hyperbolic systems

Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

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Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems