Delay Partitioning Approach Research Articles

Secure Filter Design of Fuzzy Switched CPSs With Mismatched Modes and Application: A Multidomain Event-Triggered Strategy

This article investigates the finite-time secure filter design of fuzzy switched cyber-physical systems equipped with a resource-constraint network that may undergo false data injection attacks (FDIAs). To strike a higher level balance between the resource consumption and filtering performance, a multidomain probabilistic event-triggered mechanism (MDPETM) is initially developed. And the mode mismatched phenomenon between the filter and the system is characterized through a delayed switching signal. Based on the MDPETM and a virtual delay partitioning approach, fuzzy mismatched secure filters are first devised whose modes could differ from the system. Then, filter-mode-dependent Lyapunov functionals are created to obtain new sufficient criteria such that the filtering error achieves finite-time boundedness with extended dissipativity subject to admissible FDIAs. The filter gains are obtained by solving a set of convex optimization problems. Finally, an application-oriented example is employed to test the effectiveness and advantages of the proposed results.

Delay partitioning approach to the delay-dependent stability of discrete-time systems with anti-windup

ABSTRACT In this digital era, the basis of every smart instrument is discrete signal models e.g. in Networked control systems, Cyber physical systems etc. It has been shown that time-delays are unavoidable during the digital implementation of an engineering system. Therefore, the stabilization of discrete time delayed systems is gaining the high importance [1–10]. Although a lot of literature is found on the stabilization of time delayed systems for a long time using the construction of proper non-negative Lyapunov functional. Recalling some existing results on this issue, the LMI-based stability conditions are obtained by its forward difference negative-definite in direction to claim the less conservative results [15–25]. In order to seek less conservative stability criteria, this paper introduces an anti-windup scheme appended with Wirtinger inequality, reciprocal convex approach and delay partitioning of a discrete-time delayed systems by using Lyapunov Krasovskii functional. To accomplish this task, delay partitioning technique may be utilized to develop improved stability conditions for the considered system. The Wirtinger-based inequality and reciprocal convex approach has been employed to derive less conservative results. On employing the delay partitioning, a novel linear matrix inequality-based criterion is proposed to stabilize such systems. The considered Lyapunov-Krasovskii functional includes the information of intermediate delay to acknowledge the delay information implicitly that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. The estimation of the attraction basin is to ensure that the state remains inside the level set of a certain Lyapunov function. Numerical simulation verifies that the presented method reduces conservatism than the existing results.

Formula omitted] stabilization problem for memristive neural networks with time-varying delays

This work explores memristive neural networks’ (MNNs) stability and stabilization problems by considering the time-varying delay and external disturbance. First, the MNNs were transformed into a tractable model by defining the logical switched functions, paving the way to utilize the robust analysis method for the associated connection weights. Second, by proposing a new Lyapunov–Krasovskii functional constructed by the delay-partitioning approach and the free weight matrices, the exponential stability (ES) problem of the transformed MNNs model is investigated. Third, the state feedback controller’s design scheme is devised to ensure the ES of the overall closed-loop system with a prescribed H∞ disturbance attenuation performance level γ. The results are formed in terms of linear matrix inequalities. Finally, two suitable examples express the efficacy of the proposed results.

Improved stability criterion for distributed time-delay systems via a generalized delay partitioning approach

<abstract><p>This paper researches the problem of stability analysis for distributed time-delay systems. A newly augmented Lyapunov-Krasovskii functional (LKF) is first introduced via a generalized delay partitioning approach. Then, a less conservative stability criterion is derived by introducing a novel Jensen inequality to estimate the integral terms in the derivative of LKF. The stability condition is given in terms of linear matrix inequality. Finally, the merits of the obtained stability criterion is shown by a well-known example.</p></abstract>

<i>H</i>∞ performance analysis and switching control design for uncertain discrete switched time-delay systems

The H∞ performance analysis and switching control of uncertain discrete switched time-delay systems with linear fractional perturbations are studied in this paper. The design of a simple switching signal is developed to acquire LMI conditions which achieve H∞ performance and switching control of discrete switched time-delay system. The conservativeness of obtained results can be improved by using the delay-partitioning approach. The using LMI variables number is less than our past proposed non-negative inequality approach. Finally, we use some numerical examples to illustrate the major improvement of the developed results.

<i>H</i>∞ performance analysis and switching control design for uncertain discrete switched time-delay systems

The H∞ performance analysis and switching control of uncertain discrete switched time-delay systems with linear fractional perturbations are studied in this paper. The design of a simple switching signal is developed to acquire LMI conditions which achieve H∞ performance and switching control of discrete switched time-delay system. The conservativeness of obtained results can be improved by using the delay-partitioning approach. The using LMI variables number is less than our past proposed non-negative inequality approach. Finally, we use some numerical examples to illustrate the major improvement of the developed results.

Delay partitioning approach to the robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delays

This paper is associated with the problem of robust stability of discrete-time systems with time-varying delays and finite wordlength nonlinearities. The main contribution of the paper is two-fold. First, this paper presents a new Lyapunov function based on the idea of partitioning the delay interval into subintervals. The approach may be considered as an advancement over the several existing approaches where only the lower delay bound is partitioned. The second is that reciprocally convex inequality (RCI) and Wirtinger-based inequality (WBI) are used to estimate the sum terms involved in the forward difference of Lyapunov function. The intermediate delay is also included in the Lyapunov function to deal with the delay information more effectively. Finally, several examples are provided to illustrate the less conservatism of the proposed approach as compared to several existing results.

Novel robust stability condition for uncertain systems with interval time-varying delay and nonlinear perturbations

In this paper, the problem of robust stability analysis for a class of uncertain systems with interval time-varying delay and nonlinear perturbations is studied. In order to develop a less conservative stability condition, a Lyapunov-Krasovskii functional (LKF) comprising quadruple-integral term is introduced. A novel delay dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by using a new delay-partitioning approach and reciprocally convex combination technique, which is derived by integral inequality approach (IIA). Compared with the existing literature, this criterion can greatly reduce the complexity of theoretical derivation and computation. Finally, three well-known numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion.

Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller

In this paper, exponential synchronization of semi-Markovian coupled neural networks (NNs) with bounded time-varying delay and infinite-time distributed delay (mixed delays) is investigated. Since semi-Markov switching occurs by time-varying probability, it is difficult to capture its precise switching signal. To overcome this difficulty, a tracker is used to track the switching information with some accuracy. Then a quantized output controller (QOC) is designed by using the tracked information. Novel Lyapunov–Krasovskii functionals (LKFs) with negative terms and delay-partitioning approach, which reduce the conservativeness of the obtained results, are utilized to obtain LMI conditions ensuring the exponential synchronization. Moreover, an algorithm is proposed to design the control gains. Our results include both those derived by mode-dependent and mode-independent control schemes as special cases. Finally, numerical simulations validate the effectiveness of the methodology.

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results.

Secondary delay-partition approach to finite-time stability analysis of delayed genetic regulatory networks with reaction–diffusion terms

This paper investigates the finite-time stability analysis of delayed genetic regulatory networks (GRNs) with reaction–diffusion terms under Dirichlet boundary conditions. The time delays are bounded with lower and upper bounds, where the lower bounds can be zero or non-zero. Some new triple integral terms are constructed in the Lyapunov–Krasovskii functional (LKF) and the secondary delay partition method is utilized to obtain the less conservative stability criteria for GRNs. The integral ranges also have the corresponding divisions according to the time delays. Furthermore, the optimized integral inequalities, such as the Jensen’s integral inequality, Wirtinger-type integral inequality and Gronwall inequality, are applied to handle integral terms. Finally, a numerical example is presented to demonstrate the feasibility and effectiveness of the proposed criteria.

Dissipative criteria for Takagi\u2013Sugeno fuzzy Markovian jumping neural networks with impulsive perturbations using delay partitioning approach

In this work, we investigate the result of dissipative analysis for Takagi–Sugeno fuzzy Markovian jumping neural networks with impulsive perturbations via delay partition approach. By using the Lyapunov–Krasovskii functional and delay partition approach, we derive a set of delay-dependent sufficient criteria for obtaining the required results. Furthermore, we restate the obtained sufficient conditions in the form of linear matrix inequalities (LMIs), which can be checked by the standard MATLAB LMI tool box. The main advantage of this work is reduced conservatism, which is mainly based on the delay partition approach. Finally, we provide numerical examples with simulations to demonstrate the applicability of the proposed method.

Synchronization control design for uncertain coronary artery time-delay system with input saturation

A synchronization control scheme is proposed for uncertain coronary artery system (CAS) with input saturation. In order to deal with the input saturation, linear matrix inequalities (LMIS), adequate conditions are obtained based on the local sector condition. Furthermore, by constructing Lyapunov–Krasovskii functional (LKF), we design a state feedback controller to achieve synchronization for chaos system with input saturation. Moreover, the improved Jensen inequality, convex analysis, delay-partitioning approach and Moon et al.’s inequality are utilized to get the less conservative. Finally, the simulation result is given to explain the effectiveness of the proposed synchronization control scheme.

Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.

Stability analysis of wide area power system under the influence of interval time-varying delay

ABSTRACTIn view of the problem that time delay always existing in wide area power system can cause severe effects on the operation performance of the whole system, this paper studies the stability of the wide area power system with interval time-varying delays. Firstly, the model of wide area power system with interval time-varying delay is established, based on that, a new augmented vector and new Lyapunov-Krasoskii functional (LKF) are constructed. Then, the delay-partitioning approach, Wirtinger integral inequality, free-matrix-based inequality and convex combination approach are used to estimate the derivative of the functional, and as a result, a less conservative stability criterion for the delayed power system is obtained. Finally, numerical simulations of the typical second-order system, the single machine system and two-area four-generator power system are given to illustrate that the proposed method in this paper expands the stability margin of the system effectively.

Synchronization Control of Riemann-Liouville Fractional Competitive Network Systems with Time-varying Delay and Different Time Scales

This paper is concerned with a class of Riemann-Liouville fractional-order competitive neural networks with time-varying delay and different time scales. Based on delay-partitioning approach, we construct two suitable Lyapunov functionals including fractional integral terms, respectively, and avoid computing their fractional-order derivatives to derive the synchronization conditions. The sufficient conditions are proposed to ensure the complete synchronization between fractional-order response system and fractional-order derive system. By solving the algebraic equalities or linear matrix inequalities (LMIs), the design of the gain matrix of the linear feedback controller can be realized. An illustrative example is also presented to show the validity and feasibility of the theoretical results.

A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays

Two recent Lyapunov-based methods: delay-partitioning approach and Jensen inequality approach, have reduced the conservatism and the complexity of the stability result for one-dimensional (1-D) time-delay systems, respectively. This paper concerns the analysis of delay-dependent stability for two-dimensional (2-D) discrete systems with interval time-varying delays. By applying a delay partitioning-based Lyapunov function combining with the approaches of 2-D Jensen inequalities, a new delay-dependent stability criterion is derived in terms of linear matrix inequality (LMI). In addition to delay dependence, the obtained criterion is also dependent on the partition size. It is rigorously proved that the authors’ result reduces the conservativeness and computational burden than some recent ones. Numerical examples show the effectiveness and advantage of our result.

An Improved Reciprocally Convex Inequality and Application to Stability Analysis of Time-Delay Systems Based on Delay Partition Approach

In this paper, the problem of stability analysis for linear continuous-time systems with constant discrete and distributed delays is investigated. First, an improved reciprocally convex lemma is presented, which is a generalization of the existing reciprocally convex inequalities and can be directly applied in the case that of the delay interval is divided into $N\geq 2$ subintervals. Second, combining this with the auxiliary functions-based integral inequalities and the delay partition approach, a novel stability criterion of delay systems is given in terms of linear matrix inequalities. Finally, three numerical examples are given and their results are compared with the existing results. The comparison shows that the stability criterion proposed in this paper can provide larger upper bounds of delay than the other ones.

Stability analysis of uncertain neutral systems with discrete and distributed delays via the delay partition approach

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.

Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach

ABSTRACTIn this paper, we addressed the problem of stability analysis for a class of generalised mixed delayed neural networks by delay-partitioning approach. A novel integral inequality is developed by employing Wirtinger's integral inequality and Leibniz–Newton formula. By constructing an augmented Lyapunov–Krasovskii functional with triple and quadruple integral terms and using some standard integral inequality techniques, asymptotic stability criterion is obtained to the concerned neural networks. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered generalised neural networks are derived in terms of a dynamic system with sampling. Finally, numerical examples are given to show that the proposed method is less conservative than existing ones.