Large Delay Periods Research Articles

Exponential Stability of Delayed Generalized Neural Networks With Intermittent Large-Delay Periods

This article investigates the exponential stability of generalized neural networks (GNNs) with a time-varying delay. Different from the literatures on the similar topic, the considered time delay contains a few intermittent large-delay periods (LDPs). A new approach is proposed to determine how frequent and how long the LDPs are allowed for guaranteeing the exponential stability by using switching techniques. The GNN is first modeled as a switched time-delay system which may include an unstable subsystem. Then, based on a novel Lyapunov–Krasovskii functional with LDP-based terms, a delay-dependent exponential stability criterion and associated evaluation algorithm are developed. Finally, two numerical examples are provided to show the effectiveness of the proposed method.

Leader-following consensus for nonlinear multiagent systems with large delays

This paper considers the leader-following consensus problem for nonlinear multiagent systems with large delays. The time delays switch alternately between two different kinds of delays, called a small delay and a large delay. New Lyapunov functionals that depend on graph information are constructed. To guarantee the desired leader-following consensus, the concepts of the length and frequency of the large delay periods are introduced. Sufficient conditions for consensus are given in terms of linear matrix inequalities. Furthermore, low-dimensional criteria that are easily implemented especially for large-scale multiagent systems are provided. Finally, two simulation examples are presented to validate the effectiveness of the proposed scheme.

Delay-Dependent Robust Finite-Time $$H_{\infty }$$ H ∞ Control for Uncertain Large Delay Systems Based on a Switching Method

The robust finite-time $$H_{\infty }$$ control for a kind of uncertain delay systems with large delay period (LDP) is discussed in this paper. First, a switching technique is exploited to transform the original system into a switched delay system. Second, within the limitation of frequency and length rate of LDP, a state feedback controller is designed to guarantee that the closed-loop system is robust finite-time bounded. Third, the finite-time $$H_{\infty }$$ performance analysis for the closed-loop system is developed. Finally, two examples are presented to clarify the validity of the proposed approach.

Stability and L1-gain analysis for positive delay systems with large delay period

In this paper, the problems of stability and [Formula: see text]-gain performance analysis for positive delay systems with large delay period are investigated. The maximum allowed delay bound is expanded. Under the limitations of frequency and length rate of the large delay period, the sufficient conditions guaranteeing stability of the considered system are obtained and the weighted [Formula: see text]-gain performance analysis is established. Detailed proofs are presented by using co-positive Lyapunov–Krasovskii functional candidates with large delay integral terms and the switching method; where the switching method involves transforming the original system into a positive switched delay system. All the obtained conditions can be solved via linear matrix inequalities. Finally, the validity of the proposed results is illustrated by a numerical example.

Extended Finite-Time Boundedness and Stability for Switched Linear Systems with Large Delay Period

In this paper, finite-time stability (FTS) and finite-time boundedness (FTB) are investigated for a class of switched linear systems with large delay period and input disturbances. The limitation of the frequency and the maximum ratio of large delay period are used to guarantee the properties of FTS and FTB. By constructing a piecewise Lyapunov functional with large delay integral terms, sufficient conditions that can guarantee the FTS and FTB are developed in the form of linear matrix inequalities. Two numerical examples are provided to demonstrate the effectiveness of the proposed results.

Stabilization for linear uncertain systems with switched time-varying delays

This paper is concerned with the robust stabilization problem for a class of uncertain linear time-delay systems with large delay periods. The aim of this paper is to design a state feedback controller such that the closed-loop system is exponentially stable and preserves a desired performance in the presence of large delays. In order to deal with the large delay periods, the original system is converted into a switched delay system, in which the delays are time-varying. The delay-dependent condition is established in terms of matrix inequalities. The desired controllers can be solved by the cone complementary linearization method. An example is presented to illustrate the effectiveness of the proposed technique.

Observer‐based H ∞ stabilisation for linear systems with large delay periods

This study is concerned with the observer-based H ∞ stabilisation problem for a class of linear systems with large delay periods (LDPs). Based on the switching technique, the system with LDPs is modelled into a switched delay system which consists of two subsystems. The controller and observer gains are solved under the small delay case. Sufficient conditions are derived to ensure the system is not only exponentially stable, but also possesses an H ∞ performance index. The effectiveness of the proposed method is validated by the simulation of a load frequency control system.

Guaranteed cost load frequency control for a class of uncertain power systems with large delay periods

This paper investigates the problem of guaranteed cost load frequency control (LFC) for a class of uncertain power systems with large delay periods (LDPs). The model of LFC for power systems with LDPs has been firstly modeled as a switched delay system, which includes a potentially unstable subsystem caused by LDPs and a stable subsystem caused by small delay periods (SDPs). Based on the switching technique and under the constraint conditions of the length ratio and the frequency of LPD, the guaranteed cost load frequency controller can be obtained such that the closed-loop system is exponentially stable and a weighted guaranteed cost upper bound is achieved. Finally, an example is provided to demonstrate the applicability of the proposed method.

Exponential stability of descriptor systems with large delay period based on a switching method

This paper addresses the problem of exponential stability for a class of descriptor systems with interval time-varying delays. The time-varying delays contain a large delay period (LDP), which is often present in practical control systems. Such descriptor system with LDP has been modeled as a switched descriptor system with delay, which may include an unstable subsystem caused by large delay bound. By adopting the switching technique and constructing a novel Lyapunov–Krasovskii functional, stability criteria are proposed under the restriction frequency and the rate of LDP to ensure that the descriptor system is regular, impulse free and exponentially stable. Finally, an integrated circuit example and a numerical simulation are given to illustrate the effectiveness and applicability of the proposed method.

Input-to-State Stability for Nonlinear Systems With Large Delay Periods Based on Switching Techniques

The paper is concerned with the problem of input-to-state stability (ISS) for nonlinear delay systems with large delay periods (LDP). The concepts of the length rate of LDP and the frequency of LDP are introduced. First the considered system is converted into a switched delay system which may include an unstable subsystem. Then based on a piecewise Lyapunov functional, the ISS properties of the systems are developed under the constraints of the length rate and the frequency of LDP. ISS for a special kind of nonlinear delay systems is also considered and the conditions of nonlinear matrix inequalities (NLMIs) are proposed to guarantee the ISS properties of such a system. A numerical example and an example of a series DC motor are given to show the effectiveness of the proposed methods.

Stability analysis for networked control systems based on average dwell time method

AbstractThis paper studies the problem of the exponential stability of networked control systems (NCSs) with large delay periods, which often appear in the transmission of NCSs. Some new concepts about large delay periods are introduced, and a method based on switching is employed. The maximum allowable transfer interval is obtained such that the considered system is exponentially stable. The criteria obtained contain existing results without considering a large delay period as a special case. An example is given to show the effectiveness of the proposed criteria. Copyright © 2009 John Wiley & Sons, Ltd.