Interval Time-varying Delay Research Articles

P.094 Evaluate effects of pimavanserin on anxious depression in patients with major depressive disorder - secondary analysis of the CLARITY Study

This paper is devoted to stability analysis of continuous-time delay systems with interval time-varying delays having known bounds on the delay derivatives. A parameterized family of Lyapunov–Krasovskii functionals involving multiple integral terms is introduced, and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time-varying delays. The efficiency of the proposed method is illustrated by numerical examples.

Further results on delay-dependent robust H ∞ control for uncertain systems with interval time-varying delays

This work focuses on the delay-dependent robust H ∞ control for uncertain linear systems with interval time-varying delays. The key features of the method include employment of a tighter integral inequality and construction of an appropriate Lyapunov–Krasovskii functionals (LKF). Meanwhile, the delay-dependent conditions with less conservatism are derived owing to the consideration of the information of the lower bound of time delay. Based on the obtained criteria, robust H ∞ controller design and performance analysis for the uncertain system are presented. Some numerical examples are also provided to show the effectiveness and advantage of the main results.

Improved Delay-Dependent Stability Criterion for Genetic Regulatory Networks with Interval Time-Varying Delays via New Lyapunov Functionals

In this work, the stability analysis problem of the genetic regulatory networks (GRNs) with interval time-varying delays is presented. In the previous works, the constructions of Lyapunov functional have usually been in simple Lyapunov functional, augmented Lyapunov functional, and multiple integral Lyapunov functional. Therefore, we introduce new Lyapunov functionals expressed in terms of delay product functions. New delay-dependent sufficient conditions for the genetic regulatory networks (GRNs) are established in the terms of linear matrix inequalities (LMIS). In addition, a numerical example is provided to illustrate the effectiveness of the theoretical results.

Robust local stabilization of discrete time-varying delayed state systems under saturating actuators

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.

Event‐triggered load frequency control for multi‐area power systems based on Markov model: a global sliding mode control approach

In this study, a new method is put forward for the stability and stabilisation analysis of the event-triggered load frequency control (LFC) with interval time-varying delays, considering the global sliding mode controller. To lighten the network bandwidth and save more limited networked resources, the event-triggered scheme is optimised through quantum genetic algorithm, according to different circumstances. Additionally, global sliding mode control (GSMC) scheme is proposed to provide stronger robustness performance, which against the frequency deviation caused by power unbalance or transmission time delays better. Based on the proposed schemes, multi-area LFC for the power system model is formulated as a Markov jump linear system model, considering transmission time delays and external disturbances. By applying improved Lyapunov stability theory, criteria about the stability and stabilisation conditions for multi-area power system can be deduced in terms of linear matrix inequality. Finally, to validate a more realistic LFC application, the proposed event-triggered GSMC is also deployed on Kundur's two-area test system. Simulation studies are carried out to illustrate the effectiveness and superiority of the developed schemes.

Guaranteed Cost Control of Uncertain Networked Control Systems With a Hybrid Communication Scheme

This paper proposes a guaranteed cost control method for uncertain networked control systems with a hybrid communication scheme. First, a hybrid communication scheme including time-triggered control and periodic event-triggered control (ETC) is presented for the system under consideration. The major features of the proposed scheme include three aspects: 1) instead of a fixed switching process, the switching between two triggering methods is stochastic satisfying Bernoulli distribution; 2) the condition of ETC utilizes a more recently transmission data packet, which results in reducing the transmission frequency of sampled data than some existing ones; and 3) Zeno phenomenon can be excluded since the minimum interevent time is implicity denoted by the sampling period. Second, the closed-loop system subject to the hybrid communication scheme and network-induced delay is modeled as an uncertain stochastic system with an interval time-varying delay. Two theorems are presented for the robustly mean-square stability and guaranteed cost controller design of the derived system. Then, a minimization problem is proposed to optimize the upper bound of cost function, in which the trigger parameters and feedback gain can be designed simultaneously. Finally, the effectiveness of the proposed method is demonstrated through a practical inverted pendulum on a cart.

Exponential admissibility analysis for singular systems with time-varying delay based on a parameter-dependent reciprocally convex inequality

This paper is concerned with the exponential admissibility problem of singular systems with interval time-varying delay. A parameter-dependent reciprocally convex inequality (PDRCI) is developed, which covers some existing ones as its special case. By using the system decomposition method, the considered system is decomposed into differential equations and algebraic ones. Unlike some existing works, the components of state vectors of the subsystems are applied to construct a new augmented Lyapunov–Krasovkii functional (LKF) with fewer decision variables. Based on the new integral inequality and augmented LKF, two exponential admissibility criteria are obtained in terms of linear matrix inequalities (LMIs). It should be mentioned that the derivative of the time-varying delay does not need to be smaller than one in this paper. The effectiveness of the proposed methods is demonstrated by two examples.

Exponential synchronization of stochastic delayed memristive neural networks via a novel hybrid control

This paper investigates the exponential synchronization issue of stochastic delayed memristive neural networks (SDMNNs) via a novel hybrid control (HC), where impulsive instants are determined by the state-dependent trigger condition. The switching and quantification strategies are applied to the event-based impulsive controller to cope with the challenges induced concurrently by interval parameters, impulses, stochastic disturbance and time-varying delays. Furthermore, the control costs can be reduced and communication channels and bandwidths can be saved by using this designed controller. Then, novel Lyapunov functions and new analytical methods are constructed, which can be used to realize the exponential synchronization of SDMNNs via HC. Finally, a numerical simulation is provided to demonstrate our theoretical results.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

New finite-time stability analysis of singular fractional differential equations with time-varying delay

Abstract The Lyapunov function method is a powerful tool to stability analysis of functional differential equations. However, this method is not effectively applied for fractional differential equations with delay, since the constructing Lyapunov-Krasovskii function and calculating its fractional derivative are still difficult. In this paper, to overcome this difficulty we propose an analytical approach, which is based on the Laplace transform and “inf-sup” method, to study finite-time stability of singular fractional differential equations with interval time-varying delay. Based on the proposed approach, new delay-dependent sufficient conditions such that the system is regular, impulse-free and finite-time stable are developed in terms of a tractable linear matrix inequality and the Mittag-Leffler function. A numerical example is given to illustrate the application of the proposed stability conditions.

Synthesizing Sparse and Delay-Robust Distributed Secondary Frequency Controllers for Microgrids

Consensus-based control schemes experience increasing popularity in the context of secondary frequency control in microgrids. Fundamental aspects in their practical implementation are the design of the communication topology as well as robustness with respect to both time-varying communication delays and exogenous disturbances. Motivated by this, we propose a design procedure for a consensus-based secondary frequency controller that ensures robustness with respect to heterogeneous fast-varying communication delays and simultaneously provides the option to trade off the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain performance against the number of required communication links. Our design criterion is equilibrium-independent and based on the Lyapunov-Krasovskii method for interval time-varying delays together with the descriptor method. The efficacy of the proposed approach is demonstrated by using numerical experiments on the CIGRE benchmark medium-voltage distribution network.

Event-Triggered Fuzzy Filtering for Networked Systems With Application to Sensor Fault Detection

This article concerns the event-triggered fault detection filtering problem for nonlinear networked control systems. First, an event-triggered scheme with two trigger matrices is proposed by considering limited network resources; a fuzzy fault detection filter with a general structure is chosen as the residual generator. Then, we introduce a new event-based residual system by taking into consideration the interval time-varying delays. Sufficient conditions are obtained to guarantee that the event-based residual system is asymptotically stable and satisfies a prescribed $\mathcal {H}_{\infty }$ performance with the help of a reciprocally convex technique. Furthermore, some new relaxation matrices are introduced such that the corresponding solvability conditions can be established by means of a linearization procedure. Finally, examples are given to illustrate the effectiveness and advantages of the proposed new fault detection filtering techniques.

Stability analysis of neutral systems with mixed interval time-varying delays and nonlinear disturbances

This paper studies the problem of stability analysis for neutral systems with mixed time-varying delays and nonlinear disturbances. Improved stability criteria are obtained by applying augmented Lyapunov-Krasovskii methodology. First, a novel Lyapunov–Krasovskii functional containing the intersection relationship terms about mixed time-varying delays and their upper-lower bounds with lower bounds limited to be strictly greater than zero is fully established. Second, the upper bounds for integral terms presented are accurately estimated based on integral intervals decomposition approach. Third, a less conservative stability condition in terms of linear matrix inequality is derived by utilizing a new quadratic inequality technology. In the end, two numerical examples are given to illustrate the effectiveness and the advantages of the proposed method.

Stability Analysis of Systems with Interval Time-Varying Delays via a New Integral Inequality

This paper focuses on delay-dependent stability analysis for systems with interval time-varying delays. Based on a new integral inequality and a generalized reciprocally convex combination matrix inequality, a new delay-dependent stability criterion is obtained in terms of a linear matrix inequality (LMI). Finally, the merits of the proposed criterion are shown by two numerical examples.

Stability Analysis and Robust H∞ Controller Synthesis with Derivatives of Membership Functions for T-S Fuzzy Systems with Time-varying Delay: Input-output Stability Approach

This paper investigates the problem of delay dependent stability and H∞ control design with derivatives of membership functions of uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. A model transformation is employed by considering a three-term approximation of delayed state vector. Using Scaled Small Gain (SSG) theorem and fuzzy weighting-dependent Lyapunov functions with some useful slack variables, less conservative robust stability and stabilization criteria are formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by using standard numerical packages. Finally, numerical experiments are presented to illustrate the effectiveness of the proposed method.

Impulsive and pinning control synchronization of Markovian jumping complex dynamical networks with hybrid coupling and additive interval time-varying delays

This study examines the problem of impulsive and pinning control synchronization of Markovian jumping master-slave complex dynamical networks with hybrid coupling and additive interval time-varying delays. The linear couplings include both the discrete time-varying delay and the distributed time-varying delays. Two kinds of control schemes are utilized to synchronize the considered dynamical network system. Impulsive and pinning control strategies are designed to synchronize the master-slave complex networks. By applying Lyapunov stability theory, Jensen’s inequality, Schur complement and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the asymptotic stability of this system. We provided numerical examples to illustrate the feasibility and effectiveness of the results obtained.

Delay-Dependent $H_\infty$ Guaranteed Cost Control for Uncertain Switched T–S Fuzzy Systems With Multiple Interval Time-Varying Delays

This article deals with delay-dependent H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> guaranteed cost control for uncertain switched Takagi-Sugeno (T-S) fuzzy systems with multiple interval time-varying delays. It is the first time that the fault tolerant control (FTC) of nonlinear systems subject to measurement noise, external disturbances, nonlinear functions, and intermittent faults (IFs) in sensors and actuators is investigated. A passive dynamic full-order output feedback controller is first addressed for the system to guarantee the exponential stability. Compared with the existing results, the restrictions on the multiple time-varying delays are relaxed in the derivation of this work. The suggested controller has a wider application. Moreover, as the piecewise fuzzy Lyapunov function is introduced with some slack matrices, the delay-dependent sufficient conditions are provided in the way of a cluster of linear matrix inequalities (LMIs) and then less conservatism is attained by our design contrast to the existing fault tolerant controllers. At last, two simulation examples and some comparisons are achieved to illustrate the novelty and feasibility of the method gathered in the article.

Robust H∞ filtering for finite-time boundedness of Markovian jump system with distributed time-varying delays

This paper is concerned with the problem of the guaranteed filtering with interval time-varying delay and Markovian jumping system. By constructing Lyapunov–Krasovskii functional, a novel delay-dependent criterion is presented such that the error system is stochastically finite-time bounded. In order to obtain results, Jensen's inequality, Wirtinger's integral inequality and Auxiliary function-based integral inequalities are employed. The filter matrix can be achieved by solving the linear matrix inequalities (LMIs). Numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method.

Robust H∞ controller design for uncertain 2D continuous systems with interval time-varying delays

ABSTRACTThe design of delay-dependent robust controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to performance analysis and robust controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.

Receding Horizon Synchronization of Delayed Neural Networks Using a Novel Inequality on Quadratic Polynomial Functions

This article investigates H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization of delayed neural networks under a receding horizon scheme, where two types of interval time-varying delays are considered according to whether the lower bound of the delay derivative is known or not. Note that a receding horizon synchronization law can be regarded as an optimization solution at each timeslot to a minimaxization problem related closely with a certain cost functional. In this article, two cost functionals with some delay-dependent matrices are introduced, respectively, for the two types of time delays. In order to obtain less conservative conditions, a novel inequality on quadratic polynomial functions is established, which includes some existing ones as its special cases. Based on the novel inequality, two sufficient conditions are derived to design the terminal weighting matrices of the cost functionals such that the resulting synchronization error system can be stabilized with a prescribed infinite horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level. Finally, three numerical examples are used to demonstrate the validity of the proposed results.