Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays

In this paper, we consider delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed delays. Although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained, almost no stability condition for fuzzy systems with distributed delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed delays. Here we employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of fuzzy systems with discrete and distributed delays. We introduce some free weighting matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative stability conditions. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we give two examples to illustrate our results. Delay-dependent stability conditions obtained here are shown to guarantee a wide stability region.     

Robust stability analysis and stabilization for uncertain linear neutral delay systems

This paper considers the problem of robust stability analysis and robust stabilization for uncertain neutral delay systems. The system under consideration is subject to norm-bounded parameter uncertainty appearing in all the matrices of the state-space model. Both delay-dependent and -independent robust stability conditions are obtained in terms of linear matrix inequalities. Based on these, the corresponding conditions for the exsitence of robust stabilizing state feedback controllers are developed. When these conditions are feasible, the desired state feedback controller gain matrices can be obtained via convex optimization.     

一类非线性不确定时滞系统的鲁棒镇定

基于Ｌｙａｐｕｎｏｖ稳定性理论,了一类具有状态非线性不确定线性时滞系统的鲁棒稳定的一个充分条件。通过求解一个代数Ｒｉｃｃａｔｉ方程即可获得鲁棒稳定控制器,并且该控制器不依赖于系统的时滞。具体算例说明了该方法有效性。     

不确定时滞系统的鲁棒绝对稳定性研究

基于Lyapunov稳定性理论，采用线性矩阵不等式处理方法，研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题．导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件，据此可计算出最大的允许时滞界．通过求解一组线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法。     

一类线性时滞系统的鲁棒稳定性分析

针对一类具有范数有界不确定性和2个继发时变时滞的线性时滞不确定系统,研究了其时滞依赖鲁棒稳定性问题.通过定义充分利用时变时滞上下界信息的新型Lyapunov-Krasovskii泛函,并结合时滞系统相关处理方法和线性矩阵不等式方法,得到了时滞线性不确定系统鲁棒渐近稳定所满足的条件.为了降低结论的保守性,对某些项进行了较紧致的估计.此外,并未引入自由权矩阵.最后并通过2个数值仿真证实了方法的有效性和优越性.     

Robust anti-windup controller design of time-delay fuzzy systems with actuator saturations

This study presents a robust anti-windup fuzzy control approach for uncertain nonlinear time-delay systems with actuator saturations. The discussed system dynamics is presented by the Takagi-Sugeno (T-S) fuzzy model. To facilitate the design process, the nonlinearity of input saturation is characterized by a specific sector condition. Given a stabilizing dynamic output feedback fuzzy controller, an anti-windup control approach is then developed to maximize the size of estimate of the domain of attraction. Significantly, the convergence of all admissible initial states within this region could be ensured. Based on the Lyapunov-Krasovskii delay-independent and delay-dependent analyses, sufficient conditions for the robust stabilization are derived. These conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities, allowing the fuzzy controller to be synthesized more efficiently. Finally, numeric simulations are given to validate the proposed approach.     

Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays

This paper focuses on the problem of delay-dependent robust stochastic stability analysis and controller synthesis for Markovian jump systems with state and input delays. It is assumed that the delays are constant and unknown, but their upper bounds are known. By constructing a new Lyapunov-Krasovskii functional and introducing some appropriate slack matrices, new delay-dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities (LMIs). An important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays. Memoryless state feedback controllers are designed such that the closed-loop system is robustly stochastically stable. Some numerical examples are provided to illustrate the effectiveness of the proposed method.     

Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system. Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers. First, based on an integral inequality and a fuzzy Lyapunov–Krasovskii functional, a delay-dependent FTS criterion is proposed for open-loop fuzzy system by introducing some free fuzzy weighting matrices, which are less conservative than other existing ones. Then, the parallel distributed compensation controller is designed to ensure FTS of the time-delay fuzzy system. Finally, an example is given to illustrate the effectiveness of the proposed design approach.     

线性时滞系统滞后反馈鲁棒镇定

本文研究时不变线性时滞系统的鲁棒镇定问题。通过建立时滞系统的一个渐近稳定性定理，对摄动矩阵满足匹配条件和不满足匹配条件的情况分别给出了完全鲁棒镇定控制器的设计方法与鲁棒镇定控制器的存在性充分条件和设计方法；文中尤其提出了非滞后线性系统的一种简单的滞后反馈镇定方案。文末用例子示例了本文的设计方法。     

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.     

Robust stability of uncertain time-delay systems

This paper presents several sufficient conditions, delay-independent or delay-dependent, that guarantee the robust stability of uncertain time-delay systems subjected to parametric perturbations. Both single and composite uncertain systems with one delayed state are considered and each of these results, expressed by a succinct scalar inequality, permits the assessment of the transient behaviour of uncertain systems. The robustness of the time-delay system with respect to delay uncertainty is also discussed. Furthermore, these results are extended to the perturbed systems with multiple non-commensurate time delays. It is shown that the parameter perturbations may destabilize the system; hence the nominal system should be sufficiently stable to ensure robust stability.     

一类不确定时滞系统的时滞依赖型鲁棒控制器设计

本文研究了一类状态和控制同时存在滞后的不确定线性系统时滞依赖型鲁棒镇定２，针对所有容许的时变未知但有界的不确定性，得到了一种新的确保系统可鲁棒镇定的充分条件和相应的鲁棒镇定控制器设计方法，所得到的结果与时滞相关的，并且以线性矩阵不等式（ＬＭＩ）形式给出。     

基于矩阵测度的非线性广义时滞系统鲁棒模糊控制

研究T-S模糊广义时滞系统的鲁棒控制问题.不同于传统的寻求公共正定矩阵的方法,基于矩阵测度给出保证系统鲁棒稳定的充分条件,并将此条件进一步转化为线性矩阵不等式.通过求解线性矩阵不等式,得到状态反馈控制器和静态输出反馈控制器.最后通过算例仿真验证了方法的有效性.     

线性时滞不确定系统的鲁棒稳定控制

对于线性时滞不确定系统,给出一种鲁棒渐近稳定控制器的设计方法,且对匹配与不匹 配两类不确定系统进行了研究.与现有结果相比,按此方法设计的系统不但控制器增益较小, 实现方便,而且可以容许较大的系统不确定性.     

基于状态观测器的一类非线性系统的模糊鲁棒控制

利用T－S模型对一类非线性不确定系统进行模糊建模,在此基础上研究模糊鲁棒观测器及模糊状态鲁棒控制器的设计,并证明所设计的模糊鲁棒观测器和模糊状态鲁棒控制器具有全局渐近稳定性质。     

Robust passivity and passification of stochastic fuzzy time-delay systems

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.     

不确定广义系统的时滞依赖鲁棒镇定

研究不确定广义系统的时滞依赖鲁棒镇定问题。利用Lyapunov泛函方法,得到一个线性矩阵不等式(LMIs)形式的时滞依赖稳定与镇定判据。新方法考虑一些以前方法中通常忽略的有用的项,引入一些自由权重矩阵,估计Lyapunov泛函导数的上界;再用凸优化算法,进一步给出状态反馈控制器的设计方法。最后通过两个仿真示例表明了新方法的有效性。     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.