Bound Of Time-varying Delay Research Articles

Stability analysis and control synthesis for positive semi-Markov jump systems with time-varying delay

This paper deals with stability analysis and control synthesis for positive semi-Markov jump systems (S-MJSs) with time-varying delay, in which the stochastic semi-Markov process related to nonexponential distribution is considered. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing have some conservation. To deal with these problems, the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition. Then, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear Lyapunov–Krasovskii functional depending on the bound of time-varying delay. Furthermore, an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable in standard linear programming. The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs with time-varying delay under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, three examples, one of which is the virus mutation treatment model, are given to demonstrate the validity of the main results.

Synchronization of coupled reaction–diffusion neural networks with hybrid coupling via aperiodically intermittent pinning control

This paper investigates the complete synchronization for linearly coupled neural networks with time-varying delays and reaction–diffusion terms by using the aperiodically intermittent pinning control. The coupling matrix for the network can be asymmetric. Compared with state coupling in the synchronization literature, we design a novel distributed coupling protocol by using the reaction–diffusion coupling: spatial coupling, which can accelerate the synchronization process. This can be regarded as the main difference between this paper and previous works. Using the Lyapunov function and theories in the aperiodically intermittent control, we present some criteria for the complete synchronization with a static coupling strength. In this case, there is no constraint on the bound of time-varying delays, so it can be larger than the length of control span. On the other hand, we also consider the network with an adaptive coupling strength. In this case, the infimum of the control time span should be larger than the upper bound of time delay. Numerical simulations are given to show correctness of obtained results.

Exponential stability analysis and [formula omitted] synthesis of positive T-S fuzzy systems with time-varying delays

The α-exponential stability analysis and l1 controller synthesis of positive Takagi–Sugeno fuzzy discrete-time systems with time-varying delays are discussed in this paper. A sufficient condition of α-exponential stability for autonomous positive fuzzy systems is first established by constructing a new Lyapunov–Krasovskii functional, which depends on a given scalar 0<α<1 and the bound of time-varying delays. Then, a sufficient condition for controlled systems with l1 gain constraint is also presented while imposing α-exponential stability, upon which, a constrained l1 controller is designed for both single-input and multi-input cases. Finally, an example is given to show the feasibility of the theoretical results.

Consensus of feedforward nonlinear systems with a time-varying communication delay

ABSTRACTThe consensus problem of feedforward nonlinear systems under an undirected network with a time-varying communication delay is studied. In order to solve this problem, new consensus controller with an additional design parameter that can eliminate the effect of a feedforward nonlinearity and a time-varying communication delay on the consensus problem is proposed. Also, it is proved that if an upper bound of time-varying delay is known, the proposed consensus controller can always solve the consensus problem of multi-agent systems even in the presence of feedforward nonlinearity and an arbitrarily large communication delay. A numerical example is given to illustrate the validness of the proposed approach.

Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.

Event-Triggered Average Consensus for Multiagent Systems with Time-Varying Delay

The paper investigates average consensus for multiagent systems with time-varying delay. A reducing dimension multiagent systems model is presented firstly. Using event-triggered mechanism to reduce network load, a comprehensive model is then proposed, which considers communication delay and triggered issue. Furthermore, the event-triggered average consensus stability of multiagent systems with fixed directed/undirected graph is analyzed, and sufficient conditions are provided. Moreover, the upper bound of time-varying delay can be obtained conveniently. Finally, simulation results confirm the feasibility and effectiveness of the proposed method.

Average Consensus in Networks of Multi-Agent with Multiple Time-Varying Delays

The average consensus in undirected networks of multi-agent with both fixed and switching topology coupling multiple time-varying delays is studied. By using orthogonal transformation techniques, the original system can be turned into a reduced dimensional system and then LMI-based method can be applied conveniently. Convergence analysis is conducted by constructing Lyapunov-Krasovskii function. Sufficient conditions on average consensus problem with multiple time-varying delays in undirected networks are obtained via linear matrix inequality (LMI) techniques. In particular, the maximal admissible upper bound of time-varying delays can be easily obtained by solving several simple and feasible LMIs. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results.