ON BOUNDEDNESS OF SOLUTIONS OFIMPULSIVE INTEGRO-DIFFERENTIAL SYSTEMSWITH FIXED MOMENTS OF IMPULSE EFFECTS

Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.

Analysis of Higher Order System with Impulse Exciting Functions in Z-Domain

This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities （LMIs）. A numerical example is presented to illustrate the proposed methodology.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Stability and boundedness in terms of two measures for nonlinear impulsive control systems

In this paper we study stability and boundedness in terms of two measures for impulsive control systems. By using variational Lyapunov method, a new variational comparison principle and some criteria on stability and boundedness are obtained. An example is presented to illustrate the efficiency of proposed result.

Exponential stability of Takagi-Sugeno fuzzy systems with impulsive effects and small delays

This paper deals with the exponential stability of impulsive Takagi-Sugeno fuzzy systems with delay. Impulsive control and delayed fuzzy control are applied to the system, and the criterion on exponential stability expressed in terms of linear matrix inequalities （LMIs） is presented.

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.

ON THE INITIAL VALUE PROBLEMS OF FIRST ORDERIMPULSIVE DIFFERENTIAL SYSTEMS

The purpose of this paper is to study the existence and iterative approximation of minimax quasi-solutions for a class of initial value problems of first order impulsive differential systems by using monotone iterative methods.

Finite-Time Stability and Instability of Nonlinear Impulsive Systems

In this paper,the finite-time stability and instability are studied for nonlinear impulsive systems.There are mainly four concerns.1)For the system with stabilizing impulses,a Lyapunov theorem on global finite-time stability is presented.2)When the system without impulsive effects is globally finite-time stable(GFTS)and the settling time is continuous at the origin,it is proved that it is still GFTS over any class of impulse sequences,if the mixed impulsive jumps satisfy some mild conditions.3)For systems with destabilizing impulses,it is shown that to be finite-time stable,the destabilizing impulses should not occur too frequently,otherwise,the origin of the impulsive system is finite-time instable,which are formulated by average dwell time(ADT)conditions respectively.4)A theorem on finite-time instability is provided for system with stabilizing impulses.For each GFTS theorem of impulsive systems considered in this paper,the upper boundedness of settling time is given,which depends on the initial value and impulsive effects.Some numerical examples are given to illustrate the theoretical analysis.

Optimal control for a class of impulsive switched systems

In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-specified.The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes.Moreover,the subsystems do not require a refractory period,which can bring more generality.Using the calculus of variation,the partial derivatives of the cost with respect to the control variables are derived,based on which the optimality conditions are given.Meanwhile,the obtained formulas can be used in some gradient descent algorithms to locate the optimal control variables.Finally,the viability of the proposed method is illustrated through two numerical examples.

EXPONENTIAL STABILITY OF LINEAR TIME－VARYING IMPULSIVE DIFFERENTIAL SYSTEMS WITHDELAYS

This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function, some criteria of global exponential asymptotic stability for the impulsive time-delay system are established. An example is given to illustrate the applicability of the obtained results.

BOUNDEDNESS IN TERMS OF TWO MEASURES FOR IMPULSIVE DISCRETE SYSTEMS

This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principle. The result obtained generalizes those in known literatures.

CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF FRACTIONAL-ORDER IMPULSIVE SYSTEMS

This paper studies the controllability and observability for a class of fractionalorder impulsive systems.First,the basic acknowledgement of fractional-order systems is presented.Then the solution of the fractional-order impulsive systems is given.Finally,necessary and sufficient criteria for controllability and observability are obtained.

Study on Variation of Parameters Formula and Stability for Impulsive Time－Delay Nonlinear Large Scale Systems

This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.

Fault Detection for a Class of Impulsive Switched Systems

The problem of fault detection for a class of nonlinear impulsive switched systems is investigated in this paper. Fault detection filters are designed such that the augmented systems are stable, and the residual error signal generated by the filters guarantees the H∞ performance for disturbances and faults. Sufficient conditions for the design of fault detection(FD) filters are presented by linear matrix inequalities. Moreover, the filter gains are characterized according to a solution of a convex optimization. Finally, an example derived from a pulse-width-modulation-driven boost converter is given to illustrate the effectiveness of the FD design approach.

Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Existence of Solutions for Nonlinear Boundary Value Problems of Impulsive Differential Equations

With the help of the coincidence degree continuation theorem, we generalize to the case of impulsive systems of the second order some existence results obtained by Gaines and Mawhin in the ordinary case. In particular. for the impulsive functions the treatment does not assume any mono- tonicity conditions. which are necessary in earlier papers treated by S.Hu and V.Lakshmikantham, L.H.Erbe and X.Liu with other methods.

MULTIPLE POSITIVE PERIODIC SOLUTIONS IN A IMPULSIVE PREDATOR-PREY SYSTEM WITH TYPEⅣFUNCTIONAL RESPONSES

The main purpose of this paper is to explore the existence of positive periodic solutions to impulsive predator-prey systems with type IV functional responses. Sufficient criteria are obtained for the existence of strictly positive periodic solutions. The approach is based on a continuation theorem in the coincidence degree theory as well as some prior estimates. This is also the first time that multiple positive periodic solutions are obtained using coincidence degree theory in impulsive ecological systems.