Stability criteria for linear systems with multiple time-varying delays

New delay-independent and deky-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying dekys. Therefore, they are suitable for the case with very fast time-varying dekys. In addition, some remarks are also given to expkin the obtained results and to point out the limitations of the previous results in the literature.     

Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects

According to integrated pest management for pests, we investigate the dynamic behavior of a class predator–prey system with state-dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Using the Poincaré map and the properties of the Lambert W function, we prove the sufficient conditions for the existence and stability of semi-trivial solutions and positive periodic solutions. Numerical results are carried out to illustrate the feasibility of our main results.     

Positive periodic solutions of neutral predator–prey model with Beddington–DeAngelis functional response

By using a continuation theorem based on coincidence degree theory, some new sufficient conditions are obtained for the existence of positive periodic solutions for a neutral predator–prey model with the Beddington–DeAngelis functional response.     

Analytical solution for a class of linear quadratic open-loop Nash game with multiple players

In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrix can be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure.     

Positive periodic solutions for the neutral ratio-dependent predator–prey model

By using a continuation theorem based on coincidence degree theory, we obtain some new sufficient conditions for the existence of positive periodic solutions for the neutral ratio-dependent predator–prey model with Holling type II functional response.     

Permanence and almost periodic solution of two-species delayed Lotka–Volterra cooperative systems with impulsive perturbations

By applying the comparison theorem and the Lyapunov method of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution in a class of two-species Lotka–Volterra cooperative systems with impulses. The method used in this paper provides a possible method to study the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the models with impulsive perturbations in biological populations. Finally, an example and numerical simulations are given to illustrate that our results are feasible.     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

Analysis for Cohen-Grossberg neural networks with multiple delays

The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality （LMI） is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.     

Design of H ∞ control of neural networks with time-varying delays

This paper deals with the H _∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov–Krasovskii functionals, we establish new sufficient conditions for H _∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

     

Parameter-dependent Lyapunov functional for systems with multiple time delays

The separation of the Lyapunov matrices and system matrices plays an important role when one use sparameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between the terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.     

Predictor–observer-based control of systems with multiple input/output delays

This paper deals with the control of single-input–single-output linear time-delayed systems, when there are different delays in the output/input transfer function. The process can be disturbed and unstable. A new control structure is proposed, solving the problem in several steps. First, by using a stable predictor/observer the plant is stabilized, regardless the delays. On the stable plant, the multidelay plant model is considered as a single delay plant with additional disturbances. The problem of disturbance rejection is solved by using a disturbance observer approach. Finally, output tracking is achieved by a two degrees of freedom controller.     

Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

In this paper, the Takagi–Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Cohen–Grossberg type bidirectional associative memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by using LMI optimization algorithms to guarantee the asymptotic stability of uncertain Cohen–Grossberg BAM neural networks with time varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Delay-dependent robust H-infinity control for discrete-time uncertain systems with time-varying state delays

1 Introduction The analysis and synthesis of dynamic control systems with time delays is a subject of great practical and theo- retical importance, and has received considerable attention for decades (see [1,2] and references therein). Stability cri- teria can be classified roughly into two categories: delay- independent and delay-dependent [3]. Delay-independent criteria contains no information on the delay size, which, as might be expected, is generally conservative, especially when the dela…     

H ∞ output-feedback control for switched linear discrete-time systems with time-varying delays

In this paper, the problem of H _∞ output feedback control for switched linear discrete-time systems with time delays is investigated. The time delay is assumed to be time-varying and bounded. By constructing a switched quadratic Lyapunov function for the underlying system, both static and dynamic H _∞ output feedback controllers are designed respectively such that the corresponding closed-loop system under arbitrary switching signals is asymptotically stable and a prescribed H _∞ noise-attenuation level bound is guaranteed. A cone complementary linearization algorithm is exploited to design the controllers. A numerical example is presented to show the effectiveness of the developed theoretical results.     

H-infinity control for networked control systems （NCS） with time-varying delays

1Introduction Ina networkedcontrol system(NCS),a communicationnetwork connects sensors,actuators and controllers.AnNCS has many advantages over the point_to_pointcommunication of traditional control systems:fast and easymaintenance,low cost,greater flexibility,etc.Therefore,NCSs are increasingly being usedfor industrial control in avariety of fields[1,2].On the other hand,control loopsonthe communication network are closedin an NCS.Thetime delays that occur when information is transmitte…     

Efficient solution of a class of location–allocation problems with stochastic demand and congestion

We consider a class of location–allocation problems with immobile servers, stochastic demand and congestion that arises in several planning contexts: location of emergency medical clinics; preventive healthcare centers; refuse collection and disposal centers; stores and service centers; bank branches and automated banking machines; internet mirror sites; web service providers (servers); and distribution centers in supply chains. The problem seeks to simultaneously locate service facilities, equip them with appropriate capacities, and allocate user demand to these facilities such that the total cost, which consists of the fixed cost of opening facilities with sufficient capacities, the access cost of users׳ travel to facilities, and the queuing delay cost, is minimized. Under Poisson user demand arrivals and general service time distributions, the problem is set up as a network of independent M/G/1 queues, whose locations, capacities and service zones need to be determined. The resulting mathematical model is a non-linear integer program. Using simple transformation and piecewise linear approximation, the model is linearized and solved to ϵ-optimality using a constraint generation method. Computational results are presented for instances up to 400 users, 25 potential service facilities, and 5 capacity levels with different coefficients of variation of service times and average queueing delay costs per customer. The results indicate that the proposed solution method is efficient in solving a wide range of problem instances.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.