Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

ANALYSIS OF DISTURBANCES REJECTION FOR LUR'E SYSTEMS

The analysis of disturbance rejection for singe-input singe-output(SISO) Lur'e system with norm uncertainty was concerned through invariant set analysis using Liapunov function method. The conditions on robust ellipsoidal attractor for uncertain Lur'e systems were given in terms of LMIs (Linear Matrix Inequality), which simultaneously ensure the absolute stability and disturbance rejection of the uncertain Lur'e systems.An estimate of the maximum set included in a robust ellipsoidal attractor was also presented.Finally, a numerical example was worked out to illustrate the main results.

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR'E SYSTEMS

An impulsive control scheme of the Lur' e system and several theorems on stability of impulsive control systems was presented,these theorems were then used to find the conditions under which the Lur' e system can be stabilized by using impulsive control with varying impulsive intervals.The parameters of Lur' e system and impulsive control law are given,a theory of impulsive synchronization of two Lur' e system is also presented. A numerical example is used to verify the theoretical result.

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality （LMI） via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.

An Improved Approach to Delay-dependent Robust Stabilization for Uncertain Singular Time-delay Systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality （LMI）. Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Non-fragile observer-based passive control for descriptor systems with time-delay

This paper investigates the problem of non-fragile observer-based passive control for descriptor systems with time-delay. The perturbations in both the control gain and observer gain of the observer-based controller are considered. For the cases of the additive perturbations and multiplicative perturbations, sufficient conditions are given such that the closed-loop systems are admissible and passive with dissipation η. The observer-based controller gains could be obtained from the solutions of linear matrix inequalities （LMIs）. Moreover, the maximum dissipation of the system is provided. Simulation examples are given to show the effectiveness of the deign methods.

Robust adaptive control for interval time-delay systems

This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.

On Delay-independent Stability Criteria for Linear Time-delay Systems

Several LMI representations for delay-independence stability are proposed by applying Projection Lemma and the socalled ＂Small Scalar Method＂. These criteria realize the elimination of the products coupling the system matrices and Lyapunov matrices by introducing some additional matrices. When they are applied to robust stability analysis for polytopic uncertain systems, the vertex-dependent Lyapunov functions are allowed, so less conservative results can be obtained. A numerical example is employed to illustrate the effect of these proposed criteria.

Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties

The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.

2-D algebraic test for robust stability of time-delay systems with interval parameters

The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional （2-D） interval polynomials （2-D s-z hybrid polynomials）, proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.

New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance,auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function(ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally,numerical examples are given to show the effectiveness and the merits of the proposed method.

Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Design of unknown input observer with H_∞ performance for linear time-delay systems

A unknown input observer （UIO） design for a class of linear time-delay systems when the observer error can＇t completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method. Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated. Based on H∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities （LMI）. A design algorithm is proposed. The effective of the proposed approach is illustrated by a numerical example.

Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.

Adaptive Iterative Learning Control for Nonlinear Time-delay Systems with Periodic Disturbances Using FSE-neural Network

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion （FSE） are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions （such as global Lipschitz condition） is relaxed. Furthermore, by using appropriate Lyapunov-Krasovskii functionals, all signs in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded, and the output of the system is proved to converge to the desired trajectory. A simulation example is provided to illustrate the effectiveness of the control scheme.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

Feedback iterative learning control for time-delay systems based on 2D analysis approach

This paper deals with the iterative learning control （ILC） design for multiple-input multiple-output （MIMO）,time-delay systems （TDS）.Two feedback ILC schemes are considered using the so-called two-dimensional （2D） analysis approach.It shows that continuous-discrete 2D Roesser systems can be developed to describe the entire learning dynamics of both ILC schemes,based on which necessary and sufficient conditions for their stability can be provided.A numerical example is included to validate the theoretical analysis.