Delay Partitioning Method Research Articles

Stabilization of PMSG-based wind turbine systems with sampling information: Dynamic delay partition method

This paper addresses the novel stabilization criteria for a nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS) with sampled-data information, subject to the uncertainty and controller gain variations. In this regard, the nonlinearity in PMSG-based WTS is conferred by the Takagi–Sugeno (T–S) fuzzy systems. Next, by employing the full advantages of the variable characteristic related to the sampling pattern, a novel looped-type asymmetric augmented Lyapunov-Krasovskii functional (LKF) is developed. Then, the dynamic delay partition method is the first time to be applied for the non-fragile sampled-data control design of proposed T–S fuzzy systems. Also, the less conservativeness stabilization criteria for T–S fuzzy systems are obtained in the form of linear matrix inequality. In the end, the numerical examples confirm the applicability and efficiency of the presented results.

New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems

This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into several piecewise points through a relaxable sequence of constant numbers, are increasing at a steady rate and are not larger than 1. Secondly, to fully use the interconnection information among the delayed state vectors, a new LK-functional is constructed. Thirdly, the recently published single/multiple integral inequalities are employed to bound the derivative of the newly developed LK function. Finally, a novel stability criterion for neutral systems is developed based on the above treatment. Furthermore, a new corollary is also proposed for the condition of τ=h. The benefits and productivities of our method are demonstrated by numerical examples.

Stability analysis for systems with multiple/single time delays via a Cascade augmented L-K functional

This paper investigates stability of linear systems with multiple/single time-delays. Firstly, a three-level cascade augmented Lyapunov-Krasovskii (L-K) functional is introduced, in which interconnect information among delayed state vectors is fully taken into account. Based on a newly integral inequality and the cascade L-K functional, a novel stability criterion is derived for linear systems with multiple time-delays. Secondly, it is found that the proposed L-K functional is also suitable for linear systems with single time-delay if the delay-partitioning method is employed. This motivates us to obtain a less conservative stability condition for linear systems with single time-delay. Finally, Numerical examples are given to confirm the advantages of the proposed method.

Improved results on stability analysis of time-varying delay systems via delay partitioning method and Finsler’s lemma

This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which differently from other existing approaches, the maximum switching frequency is not required for stability analysis. Thus, by the use of augmented Lyapunov-Krasovskii functionals and the Finsler’s lemma, together with some relationships among state variables intentionally defined, the inherent conservatism can be progressively reduced by refining more and more the delay partition. The superiority of the proposed method is illustrated through two benchmark examples.

Investigation of convergence behavior on fuzzy system

This paper studies the convergence behavior of a type of T-S fuzzy system with interval time-varying delay and nonlinear perturbations. A delay partitioning method is used to construct a modified Lyapunov Krasovskii functional(LKF) including triple-integral terms and augmented factors, which is introduced from these equidistant subintervals. In addition, the Free-Matrix-Based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. Eventually, much less conservative results are presented. Numerical analyses are conducted to demonstrate the evaluation of this proposed research development.

Dissipativity analysis for Takagi–Sugeno fuzzy system with time-varying delays and stochastic packet dropouts

The dissipative stability analysis of Takagi–Sugeno fuzzy system (TSFS) is the focus of this paper via taking the effects of both delays and packet dropouts. The novel augmented Lyapunov–Krasovskii functional (LKF) is proposed via utilizing the delay-dependent matrix, which provides the information of the delay derivative bounds. By applying the dynamic delay partition method, the delay interval is divided into several variable subintervals, which takes full advantage of time-varying delay information. In addition, the randomly occurring asynchronous or synchronous controllers are put forward to enhance the design flexibility and control performance. On the basis of the new augmented LKF and improved boundary techniques, the sufficient asymptotic stability condition is derived in the form of linear matrix inequalities (LMIs). Subsequently, numerical examples are addressed to certify the feasibility and advantage of the put forward methodology.

Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an H∞ attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method.

Finite-time extended dissipative filtering for nonlinear Markovian jump systems with unknown transition rates and time-varying delays

The problem of finite-time filtering for nonlinear Markovian jump systems subject to extended dissipativity with unknown transition rates and time-varying delays is investigated in this paper. Firstly, by constructing novel Lyapunov-Krasovskii functionals and utilizing delay partitioning method, the error system is proved to be stochastically finite-time bounded and extended dissipative. Secondly, in virtue of linear matrix inequalities approach, the desired mode-dependent filter is obtained. Finally, two simulations are illustrated for the purpose of demonstrating the less conservativeness and effectiveness of the proposed method.

Formula omitted] synchronization of delayed neural networks via event-triggered dynamic output control

This paper investigates H∞ exponential synchronization (ES) of neural networks (NNs) with delay by designing an event-triggered dynamic output feedback controller (ETDOFC). The ETDOFC is flexible in practice since it is applicable to both full order and reduced order dynamic output techniques. Moreover, the event generator reduces the computational burden for the zero-order-hold (ZOH) operator and does not induce sampling delay as many existing event generators do. To obtain less conservative results, the delay-partitioning method is utilized in the Lyapunov–Krasovskii functional (LKF). Synchronization criteria formulated by linear matrix inequalities (LMIs) are established. A simple algorithm is provided to design the control gains of the ETDOFC, which overcomes the difficulty induced by different dimensions of the system parameters. One numerical example is provided to demonstrate the merits of the theoretical analysis.

Delay-dependent stability and hybrid [formula omitted]-gain analysis of linear impulsive time-delay systems: A continuous timer-dependent Lyapunov-like functional approach

This paper presents a new approach for analyzing delay-dependent stability and hybrid L2×l2-gain performance of linear impulsive delay systems. The new approach is inspired by the delay-partitioning method, the timer-dependent Lyapunov functional method, and the looped-functional method. In the delay-partitioning framework, a new type of timer-dependent Lyapunov functional is constructed, which depends on the partition on impulse intervals and also on impulse dynamics. Different from the previous discontinuous Lyapunov functionals, the introduced Lyapunov functional is continuous along the trajectories of the considered impulsive delay system. Consequently, two different problems of exponential stability and hybrid L2×l2-gain performance are tackled by using the same class of Lyapunov functionals. It is shown that the positive definiteness of this Lyapunov functional inside impulse intervals is not necessary for proving exponential stability. By use of new integral inequalities based techniques, delay-dependent criteria for exponential stability and finite hybrid L2×l2-gain are established in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach.

Delay-partitioning-based reachable set estimation of Markovian jump neural networks with time-varying delay

The objective of this paper is to estimate the reachable set for a class of delayed neural networks (NNs) subject to Markovian jump parameters and bounded disturbance. First, by virtue of delay-partitioning method, the time-varying delay is divided into some delay components. With suitably constructing Lyapunov–Krasovskii functionals (LKFs), a less conservative delay-dependent condition of finding an ellipsoid-like set to contain all state trajectories that start from the origin is derived in terms of linear matrix inequalities (LMIs). Then the integrally free-matrix-based inequality approach together with the extended reciprocally convex technique is employed to further reduce the conservatism on characterizing bounds of some integral terms. Thanks to a group of free-connection weighting matrices, the proposed reachable set estimation approach is extended to the case that transition probabilities are partially known. Finally, numerical simulations indicate that the derived results are effective and less conservative.

Reachable Set Estimation for Markovian Jump Neutral-Type Neural Networks With Time-Varying Delays.

The reachable set estimation problem for a class of Markovian jump neutral-type neural networks (MJNTNNs) with bounded disturbances and time-varying delays is tackled in this article. With the aid of the delay partitioning method, a novel stochastic Lyapunov-Krasovskii functional containing triple integral terms is constructed in mode-dependent augmented form. To begin with, transition probabilities of the concerned Markovian jump neural networks (NNs) are considered to be completely known. By employing the integral inequality approach and reciprocally convex combination method, it is proved that all state trajectories which start from the origin by bounded inputs can be constrained by an ellipsoid-like set if a group of linear matrix inequalities (LMIs) is feasible. Then, the free-connection weighting matrix technique is utilized to handle the case of partially known transition probabilities. As byproducts, some sufficient conditions are also obtained to guarantee the stochastic stability of the concerned NNs. The validity of the theoretical analysis is confirmed by numerical simulations.

Second-Order Consensus for Multi-Agent Systems With Time-Varying Delays Based on Delay-Partitioning

A consensus problem for second-order agents network with time-varying delays under the directed fixed topology is investigated in this paper. For the convenience of analysing, the original system is converted into an equivalent system associated with disagreement terms. By applying a variable delay-partitioning method, increased computational complexity is solved and obtain less conservatism. A suitable Lyapunov-Krasovskii functional (LKF) is constructed, combining the reciprocally convex combination lemmas with Wirtinger-based inequality to deal with integral items for the derivative of the LKF and further reduce the conservatism. Following the linear matrix inequality theory, a sufficient condition is presented to make all agents asymptotically reach consensus. Finally, simulations are given to illustrate the effectiveness of the proposed results.

Observer-Based Sliding Mode Control for Uncertain Fuzzy Systems via Event-Triggered Strategy

This paper investigates the problem of sliding mode observer design for a class of uncertain fuzzy time-delay systems based on an event-triggered strategy. The objective is to design an event-triggered mechanism by utilizing the information of system output and observer function. Based on the delay partitioning method and the Lyapunov–Krasovskii function approach, delay-dependent sufficient conditions are proposed to guarantee the overall system, including sliding mode dynamics and error dynamics, to be asymptotically stable with an $\mathcal {H}_{\infty }$ performance. Furthermore, an event-triggered sliding mode controller is synthesized to ensure that the system dynamics can be driven to the sliding region near the equilibrium point in finite time. Finally, a verification example is provided to demonstrate the feasibility and efficiency of the theoretical results presented.

Stability analysis for discrete-time switched GRNs with persistent dwell-time and time delays

In this paper, the problem of exponential stability for discrete-time switched genetic regulatory networks (GRNs) with persistent dwell-time (PDT) switching and time delays is concerned. The novelty of this paper is derived from introducing an extended property of quadratic convex function, and utilizing an improved summation inequality together with an extended reciprocally convex matrix inequality, which is less conservative than the Jensen inequality and the reciprocally convex combination employed in the discrete-time delay systems. In addition, the considered switching regularity is more general than dwell-time (DT) switching and average dwell-time (ADT) switching. Moreover, by introducing the delay partitioning method and the piecewise Lyapunov–Krasovskii functional, a set of sufficient conditions are established in the form of linear matrix inequalities to guarantee the discrete-time PDT switched GRNs with constant time delays and time-varying delays are exponentially stable, respectively. Finally, some numerical examples are exploited to demonstrate the validity and potential of the proposed method.

Exponential stability analysis for 2D discrete switched systems with state delays

SummaryThis paper is concerned with the delay‐dependent exponential stability analysis of two‐dimensional (2D) discrete switched systems with state delays described by the Roesser model; the delays under consideration are varying. By constructing an appropriate Lyapunov‐Krasovskii functional and using the average dwell time approach, new delay‐dependent sufficient conditions for the exponential stability of the system under study are proposed. In order to obtain less conservative conditions, the delay partitioning method is adopted as well as the free‐weighting matrix technique. The proposed conditions are formulated in the format of linear matrix inequality. The effectiveness and the reduced conservatism of the developed results are shown by illustrative examples.

Non-fragile passive control for Markovian jump systems with time-varying delays

This paper studies the problem of non-fragile passivity-based control for Markovian jump systems with time-varying delays. Based on a delay partitioning method, a modified Lyapunov–Krasovskii functional is constructed to derive sufficient conditions guaranteeing stochastic passivity of the considered systems. Moreover, a non-fragile state feedback controller is designed such that the closed-loop system is robustly stochastically passive. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

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.

Non-fragile [formula omitted] control for Markovian jump fuzzy systems with time-varying delays

This paper focuses on the non-fragile H∞ control of Markovian jump fuzzy systems with time-varying delays. In order to obtain less conservatism, an improved delay partitioning method is introduced, which divides the delay interval into multiple segments with a geometric sequence. A modified Lyapunov–Krasovskii functional is constructed and some less conservative delay-dependent stability criteria are derived by using linear matrix inequalities technique. Then a non-fragile controller is designed. Finally, two numerical examples are given to show the effectiveness of the obtained results.

Synchronization of Fuzzy Control Design Based on Bessel–Legendre Inequality for Coronary Artery State Time-Delay System

This paper investigates the problem of fuzzy state feedback control for a category of fuzzy-model-based coronary artery system(FMBCAS) with state time-delay. T-S fuzzy model is employed to close in coronary artery system(CAS) which exists unknown nonlinear characteristics. Through the use of linear matrix inequality technique, the synchronization controller for CAS are obtained. By utilizing the delay-partitioning method, we can get a less conservative results. The Bessel-Legendre inequality and the Moon’s et al. inequality with convex analysis are used to further reduce the conservatism of the system. Finally, a simulation of CAS proves the effectiveness of our strategy.