In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a th...In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.展开更多
This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient co...This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.展开更多
The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.展开更多
Based on a piecewise quadratic lyapunov function （PQLF）, this paper presents stochastic stability analysis and synthesis methods for ItO and discrete T-S fuzzy bilinear stochastic systems. Two improved stochastic st...Based on a piecewise quadratic lyapunov function （PQLF）, this paper presents stochastic stability analysis and synthesis methods for ItO and discrete T-S fuzzy bilinear stochastic systems. Two improved stochastic stability conditions have been established in terms of linear matrix inequalities （LMIs）. It is shown that the stability in the mean square for T-S fuzzy bilinear stochastic systems can be established if a PQLF can be constructed. Considering the established stability criterion, the controller can be designed by solving a set of （LMIs）, and the closed loop system is asymptotically stable in the mean square. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.展开更多
文摘In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.
基金supported by the National Natural Science Foundation of China(60374015)
文摘This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
基金This work was supported in part by the National Natural Science Foundation of China under Grant 61304063, in part by the Fundamental Research Funds for the Central Universities under Grant 72103676, in part by the Science and Technology Research Foundation of Yanan under Grant 2013-KG16, in part by Yanan University under Grant YDBK2013-12, 2012SXTS07.
文摘Based on a piecewise quadratic lyapunov function （PQLF）, this paper presents stochastic stability analysis and synthesis methods for ItO and discrete T-S fuzzy bilinear stochastic systems. Two improved stochastic stability conditions have been established in terms of linear matrix inequalities （LMIs）. It is shown that the stability in the mean square for T-S fuzzy bilinear stochastic systems can be established if a PQLF can be constructed. Considering the established stability criterion, the controller can be designed by solving a set of （LMIs）, and the closed loop system is asymptotically stable in the mean square. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.
