Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays

This paper is concerned with the problem of improved delay-dependent robust stability criteria for neutral-type recurrent neural networks (NRNNs) with time-varying delays. Combining the Lyapunov–Krasovskii functional with linear matrix inequality (LMI) techniques and integral inequality approach (IIA), delay-dependent robust stability conditions for RNNs with time-varying delay, expressed in terms of quadratic forms of state and LMI, are derived. The proposed methods contain the least number of computed variables while maintaining the effectiveness of the robust stability conditions. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.     

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay

This paper is concerned with the improved delay-range-dependent stability and robust stability criteria for linear systems with time-varying delay and norm-bounded uncertainties. In order to obtain much less conservative criteria, a Lyapunov-Krasovskii functional (LKF), which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive new stability criteria. By using delayed decomposition approach (DDA), a tighter upper bound of the derivative of Lyapunov functional can be obtained, and thus the proposed criteria give results with less conservatism compared with some previous ones. The resulting criteria have advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which are established theoretically. We show, by four well known examples, that our result overcomes the previous allowable maximum admissible upper bound (MAUB) of the time-delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay.     

Further improvement on delay-range-dependent robust absolute stability for Lur׳e uncertain systems with interval time-varying delays

This paper investigates improved delay-range-dependent robust absolute stability criteria for a class of Lur׳e uncertain systems with interval time-varying delays. By using delayed decomposition approach (DDA), a tighter upper bound of the derivative of Lyapunov functional can be obtained, and thus the proposed criteria give results with less conservatism compared with some previous ones. An integral inequality approach (IIA) is proposed to reduce the conservativeness in computing the allowable maximum admissible upper bound (MAUB) of the time-delay. The developed stability condition is expressed in terms of linear matrix inequality (LMI) that manipulates fewer decision variables and requires reduced computational load. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Improved robust stabilization method for linear systems with interval time-varying input delays by using Wirtinger inequality

This paper investigates the robust stabilization problem for uncertain linear systems with interval time-varying delays. By constructing novel Lyapunov–Krasovskii functionals and developing delay-partitioning approaches, some delay-dependent stability criteria are derived based on an improved Wirtinger׳s inequality and the reciprocally convex method. The proposed methods have improved the stability conditions without increasing much computational complexity. A state feedback controller design approach is also presented based on the proposed criteria. Numerical examples are finally given to illustrate the effectiveness of the proposed method.     

New results on delay-range-dependent stability analysis for interval time-varying delay systems with non-linear perturbations

This paper studies the problem of the stability analysis of interval time-varying delay systems with nonlinear perturbations. Based on the Lyapunov–Krasovskii functional (LKF), a sufficient delay-range-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI) and integral inequality approach (IIA) and delayed decomposition approach (DDA). Further, the delay range is divided into two equal segments for stability analysis. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Two well-known examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.     

Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay

This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.     

Further improvement on delay-range-dependent stability results for linear systems with interval time-varying delays

This paper provides an improved delay-range-dependent stability criterion for linear systems with interval time-varying delays. No model transformation and no slack matrix variable are introduced. Furthermore, overly bounding for some cross term is avoided. The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

Improved delay-range-dependent stability analysis of a time-delay system with norm bounded uncertainty

This paper presents improved robust delay-range-dependent stability analysis of an uncertain linear time-delay system following two different existing approaches – (i) non-delay partitioning (NDP) and (ii) delay partitioning (DP). The derived criterion (for both the approaches) proposes judicious use of integral inequality to approximate the uncertain limits of integration arising out of the time-derivative of Lyapunov–Krasovskii (LK) functionals to obtain less conservative results. Further, the present work compares both the approaches in terms of relative merits as well as highlights tradeoff for achieving higher delay bound and (or) reducing number of decision variables without losing conservatism in delay bound results. The analysis and discussion presented in the paper are validated by considering relevant numerical examples.     

Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks

This paper focuses the issue of robust stochastic stability for a class of uncertain fuzzy Markovian jumping discrete-time neural networks (FMJDNNs) with various activation functions and mixed time delay. By employing the Lyapunov technique and linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions are established for the robust stochastic stability of uncertain FMJDNNs. More precisely, the parameter uncertainties are assumed to be time varying, unknown and norm bounded. The obtained stability conditions are established in terms of LMIs, which can be easily checked by using the efficient MATLAB-LMI toolbox. Finally, numerical examples with simulation result are provided to illustrate the effectiveness and less conservativeness of the obtained results.     

QFT Parameter-Scheduling control design for linear Time-Varying systems based on RBF networks

For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.     

Robust stability and stabilization of fractional order linear systems with positive real uncertainty

This paper investigates the robust stability and stabilization of fractional order linear systems with positive real uncertainty. Firstly, sufficient conditions for the asymptotical stability of such uncertain fractional order systems are presented. Secondly, the existence conditions and design methods of the state feedback controller, static output feedback controller and observer-based controller for asymptotically stabilizing such uncertain fractional order systems are derived. The results are obtained in terms of linear matrix inequalities. Finally, some numerical examples are given to validate the proposed theoretical results.     

Non-fragile robust synchronization for Markovian jumping chaotic neural networks of neutral-type with randomly occurring uncertainties and mode-dependent time-varying delays

This paper deals with the problem of robust synchronization for uncertain chaotic neutral-type Markovian jumping neural networks with randomly occurring uncertainties and randomly occurring control gain fluctuations. Then, a sufficient condition is proposed for the existence of non-fragile output controller in terms of linear matrix inequalities (LMIs). Uncertainty terms are separately taken into consideration. This network involves both mode dependent discrete and mode dependent distributed time-varying delays. Based on the Lyapunov–Krasovskii functional (LKF) with new triple integral terms, convex combination technique and free-weighting matrices method, delay-dependent sufficient conditions for the solvability of these problems are established in terms of LMIs. Furthermore, the problem of non-fragile robust synchronization is reduced to the optimization problem involving LMIs, and the detailed algorithm for solving the restricted LMIs is given. Numerical examples are provided to show the effectiveness of the proposed theoretical results.     

New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning approach

This paper focuses on stability analysis and stabilization of nonlinear systems with interval time-varying delay, modeled by Takagi-Sugeno (T-S) fuzzy approach. To achieve more relaxation in the feasibility region, delay-partitioning approach is used for all integral terms in the Lyapunov-Krasovskii functional (LKF). A fuzzy Lyapunov function is proposed instead of non-integral term in LKF, and moreover, some slack matrices variables are offered to enlarge the design space. By doing this, new delay-dependent stability criteria are obtained. During the derivation of stability conditions, Jensen’s integral inequality is applied to deal with integral terms. Furthermore, in this paper the problem of controller design via the parallel distributed compensation (PDC) scheme is studied. Stability and stabilization conditions with less conservative are achieved in terms of linear matrix inequality (LMI). Finally, two numerical examples are presented to show the effectiveness of the proposed results.     

Further results on delay-range-dependent stability with additive time-varying delay systems

In this paper, new conditions for the delay-range-dependent stability analysis of time-varying delay systems are proposed in a Lyapunov–Krasovskii framework. Time delay is considered to be time-varying and has lower and upper bounds. A new method is first presented for a system with two time delays, integral inequality approach (IIA) used to express relationships among terms of Leibniz–Newton formula. Constructing a novel Lyapunov–Krasovskii functional includes information belonging to a given range; new delay-range-dependent criterion is established in term of linear matrix inequality (LMI). The advantage of that criterion lies in its simplicity and less conservative. This paper also presents a new result of stability analysis for continuous systems with two additive time-variant components representing a general class of delay with strong application background in network-based control systems. Resulting criteria are then expressed in terms of convex optimization with LMI constraints, allowing for use of efficient solvers. Finally, three numerical examples show these methods reducing conservatism and improving maximal allowable delay.     

Fractional active disturbance rejection control

A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ω_o and controller bandwidth ω_c on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.     

一种改进的时滞不确定性系统鲁棒容错控制算法

研究了一类具有时滞不确定性系统的鲁棒容错控制问题,针对既有传感器失效,又有执行器失效的故障情形,通过引入一种无记忆的状态反馈控制器,基于Lyapunov稳定定理和运用线性矩阵不等式(LMI)的方法,给出了在传感器失效和执行器失效故障下具有鲁棒完整性的充分条件,并进行了证明。最后利用Matlab中的LMI工具箱进行了算例仿真,证实了这种设计方法的有效性和可行性,减少了当出现故障时需要先判断哪类故障的任务,为容错控制提供了便利。     

Robust model predictive control for switched linear systems

Developed is a robust model predictive control scheme for a class of discrete-time switched linear systems. The system is described in linear fractional transformation form in the presence of model uncertainty and induced norm bounded disturbances. The objective is to minimize the upper bound of an infinite horizon cost function subject to a terminal inequality. A Lyapunov function analysis for the switched system shows guaranteed closed-loop stability. Taking into account the switching structure of the system, the predictive control design problem along with sufficient conditions for the existence of a solution is expressed in terms of Riccati–Metzler inequalities. Then, these inequalities are turned into a linear matrix inequality feasibility problem. Three cases are analyzed to demonstrate the performance and effectiveness of the proposed robust model predictive controller for switched discrete-time linear systems.     

Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay

This paper investigates a class of delayed cellular neural networks (DCNN) with time-varying delay. Based on the Lyapunov–Krasovski functional and integral inequality approach (IIA), a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Unlike previous methods, the upper bound of the delay derivative is taken into consideration, even if larger than or equal to 1. It is proven that results obtained are less conservative than existing ones. Four numerical examples illustrate efficacy of the proposed methods.