A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Copyright [2004] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked

Robust passivity and passification of stochastic fuzzy time-delay systems

The official published version can be obtained from the link below.In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.This work was supported by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers 200802861044, the National Natural Science Foundation of China under Grant 60804028 and the Royal Society of the United Kingdom

H ? filtering for stochastic singular fuzzy systems with time-varying delay

This paper considers the H? filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e?t - weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e?t -weighted iISSiM and the H? attenuation level from disturbance to estimation error is belowa prescribed scalar.Aset of sufficient conditions for the solvability of the H? filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out