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.     

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.     

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.     

A novel approach to delay-fractional-dependent stability criterion for linear systems with interval delay

This paper considers the problem of delay-fractional-dependent stability analysis of linear systems with interval time-varying state delay. By developing a delay variable decomposition approach, both the information of the variable dividing subinterval delay, and the information of the lower and upper bound of delay can be taken into full consideration. Then a new delay-fractional-dependent stability criterion is derived without involving any direct approximation in the time-derivative of the Lyapunov–Krasovskii (LK) functional via some suitable Jensen integral inequalities and convex combination technique. The merits of the proposed result lie in less conservatism, which are realized by choosing different Lyapunov matrices in the variable delay subintervals and estimating the upper bound of some cross term in LK functional more exactly. At last, two well-known numerical examples are employed to show the effectiveness and less conservatism of the proposed method.     

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.     

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.     

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.     

Stabilization of systems with interval time-varying delay based on delay decomposing approach

The paper considers the stabilization for systems with interval time-varying delay. By decomposing the delay interval into multiple equidistant subintervals and considering the triple integral terms, a novel Lyapunov-krasovskii functional(LKF) is defined. Then extended integral inequality and convex combination approach are used to estimate the derivative of the constructed functional, and as a result, the new stability criterion with less conservatism and decision variables is obtained. On this basis, the state feedback controller is designed, by using linearization method, the existence condition of controller is obtained in terms of linear matrix inequalities(LMIs), and the specific form of controller is also given, moreover, by selecting the appropriate parameter value, the stabilization time of the system can be reduced. Numerical examples are given to illustrate the effectiveness of the proposed method.     

New delay dependent stability criteria for recurrent neural networks with interval time-varying delay

This paper is concerned with the delay dependent stability criteria for a class of static recurrent neural networks with interval time-varying delay. By choosing an appropriate Lyapunov–Krasovskii functional and employing a delay partitioning method, the less conservative condition is obtained. Furthermore, the LMIs-based condition depend on the lower and upper bounds of time delay. Finally, a numerical example is also designated to verify the reduced conservatism of developed criteria.     

Improved delay-dependent stability analysis for neural networks with time-varying delays

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.     

Improved delay-dependent stability of neutral type neural networks with distributed delays

This paper deals with the problem of improved delay-dependent stability analysis of neutral type neural networks with distributed delays. These conditions are in terms of linear matrix inequality (LMI), easily checked by recently developed algorithms in solving linear matrix inequalities (LMIs). Finally, numerical examples demonstrate effectiveness of the proposed method.     

Identification of uncertain nonlinear systems for robust fuzzy control

In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by S?krjanc et al. (2005) [11] and [12]. With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.     

Improved stabilization method for networked control systems with variable transmission delays and packet dropout

This paper investigates the problem of stability analysis and stabilization for networked control systems with the network-induced delay and data dropout. In order to obtain less conservative results, a novel augmented Lyapunov–Krasovskii functional is introduced and new free-weighting matrices are employed to make some extra degrees of freedom in the sufficient stabilizability condition. The gain of the memoryless state-feedback controller is computed by solving a set of linear matrix inequalities (LMIs). Illustrative examples are given to verify the applicability and outperformance of the proposed method compared to the existing approaches in the literature.     

Further improved stability criteria for uncertain T–S fuzzy systems with interval time-varying delay by delay-partitioning approach

This paper focuses on further improved stability criteria for uncertain T–S fuzzy systems with interval time-varying delay by a delay-partitioning approach. A modified augmented Lyapunov–Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then some tighter bounding inequalities, i.e., Peng–Park׳s integral inequality (reciprocally convex approach) and the Free-Matrix-Based integral inequality (which yields less conservative stability criteria than the use of Wirtinger-based inequality does) are introduced to reduce the enlargement in bounding the derivative of LKF as much as possible, therefore, less conservative results can be expected in terms of e_s and LMIs. Finally, a numerical example is included to show that the proposed methods are less conservative than existing ones.     

Robust fault detection for nonlinear networked systems with stochastic interval delay characteristics

In this paper, the problem of observer-based robust fault detection (RFD) for nonlinear networked systems with stochastic interval delay is investigated. By employing the information of probabilistic distribution of networked-induced time-varying delay, the observer-based fault detection filter as residual generator and a proposed performance index as objective function, the RFD of nonlinear networked systems is formulated as an optimization problem. The desired fault detection filter is constructed in terms of certain linear matrix inequalities, which depend on not only delay-interval but also delay-interval-occurrence-rate. Especially, the sub-optimal trade-off of strong robustness from residual signal to disturbance and parameter uncertainty, as well as high sensitivity to fault is obtained by a repeated application of a two-objective optimization algorithm. Numerical simulations are given to illustrate the effectiveness of proposed techniques.     

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.