Piecewise generalised H2 controller synthesis of discrete-time fuzzy systems

Wang, Liyuan; Feng, Gang; Hesketh, T.

doi:10.1049/ip-cta:20040790

Cited by 27 publications

(17 citation statements)

References 17 publications

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“…The stability analysis results on generalized H2 (GH2) control for T-S fuzzy systems [14,15] are seldom found in the literature when compared with the H∞ control [3,12] for T-S fuzzy systems. The GH2 performance is useful for handling stochastic aspects such as measurement noise and random disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…However, the results in [16] did not include any performance criteria in the design of the control law. In addition, uncertainties and time delay have not been considered in [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the above concerns, we will consider the problem of robust GH2 control [14,15] for uncertain discretetime-delay T-S fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function. To obtain relaxed LMI conditions, for each subregion Sj, the interactions among the fuzzy subsystems are presented by one matrix Zj .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Xia

2009

Int. J. Autom. Comput.

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Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.

show abstract

Section: Introductionmentioning

confidence: 99%

“…However, the results in [16] did not include any performance criteria in the design of the control law. In addition, uncertainties and time delay have not been considered in [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Xia

2009

Int. J. Autom. Comput.

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“…The closed-loop system is described in terms of a mapping between the space of time-domain input disturbances in l 2 and the space of time-domain controlled outputs in l ∞ . Consequently, generalized H 2 performance is useful for handling stochastic aspects such as measurement noise and random disturbances (Wang et al, 2004). However, to the best of our knowledge, the problem of generalized H 2 stability analysis and controller design for T-S fuzzy large-scale systems has not been fully investigated based on PLKFs despite its theoretical and practical significance.…”

Section: Introductionmentioning

confidence: 99%

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

Xia

2011

International Journal of Applied Mathematics and Computer Science

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This paper is concerned with the problem of stochastic stability and generalized H2 control for discrete-time fuzzy largescale stochastic systems with time-varying and infinite-distributed delays. Large-scale interconnected systems consist of a number of discrete-time interconnected Takagi-Sugeno (T-S) subsystems. First, a novel Delay-Dependent Piecewise Lyapunov-Krasovskii Functional (DDPLKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, two improved delay-dependent stability conditions are established based on this DDPLKF in terms of Linear Matrix Inequalities (LMIs). The merit of the proposed conditions lies in its reduced conservatism, which is achieved by circumventing the utilization of some bounding inequalities for cross products of two vectors and by considering the interactions among the fuzzy subsystems in each subregion. A decentralized generalized H2 state feedback fuzzy controller is designed for each subsystem. It is shown that the mean-square stability for discrete T-S fuzzy large-scale stochastic systems can be established if a DDPLKF can be constructed and a decentralized controller can be obtained by solving a set of LMIs. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

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“…T-S fuzzy modeling approach is essentially a multi-model protocol in which a group of linear models are integrated to characterize the global behavior of the nonlinear system. Thanks to this particular structure, researchers can fully utilize the connections between the flexible fuzzy logic theory and fruitful linear multivariable system theory, and lots of research on systematic analysis and controller design of T-S fuzzy systems has been carried out in [23,24,25,26,27,28,29].…”

Section: Introductionmentioning

confidence: 99%

T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control of Nonlinear Systems with Actuator Faults

Wei

Qiu

Peng

et al. 2017

Circuits Syst Signal Process

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This article presents a singular approach to the reliable H ∞ static output feedback (SOF) control for continuous-time nonlinear systems with Markovian jumping actuator faults. The nonlinear plants are approximated by a Takagi-Sugeno (T-S) fuzzy-affine (FA) model with parameter uncertainties, and the Markov process is adopted to characterize the actuator-fault phenomenon. Specifically, by utilizing a singular model transformation strategy, the initially constructed closedloop system is firstly converted into a singular FA system. By constructing a Markovian Lyapunov function (MLF), together with S-procedure and some matrix inequality convexification procedures, the reliable piecewise SOF controller synthesis is then developed for the underlying systems via a convex program. Lastly, simulation examples are carried out to validate the effectiveness of the presented method.

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Piecewise generalised H2 controller synthesis of discrete-time fuzzy systems

Cited by 27 publications

References 17 publications

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

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

T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control of Nonlinear Systems with Actuator Faults

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