ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input.Secondly,in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state,slow state(smooth state)and fast state(impulsive state)are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth(slow)response and the fast(implusive)response.As a third result,a new characterization of the impulsive free initial conditions of the LNHMDEs is given.

STABILITY OF LINEAR MEASURE LARGE SCALE SYSTEMS WITH IMPULSIVE EFFECT

Many impulsive phenomena from physics, control theory, and economics urge us toinvestigate measure large scale systems. In this paper, the variation of parameters formulaof the large scale systems containing measures is established. By means of inequality methods and comparison theory, the stability, uniform stability, asymptotic stability, uniformasymptotic stability, and exponential stability properties of linear measure large scale systems are studied.

PRACTICAL STABILITY OF DYNAMIC SYSTEMS WITH IMPULISIVE SOLUTIONS

Practical stability problems of single dynamic system with impulsive solutions are considered in this paper. Using comparison principle, a class of Vk functions and impulsive differential inequalities, the criteria of practical stability, practical uniform stability and practical instability of such kind of system are obtained and proved. The results which are obtained here have improved on the results in reference [5]

Analysis and control of a non-smooth population model with impulsive effects

In this paper, a non-smooth population model with impulsive effects is proposed by combining discontinuity and non-smoothness. According to the qualitative theory of differential equations, the global analysis of the model is discussed. Using the theory of impulsive differential equations, the existence conditions of order one periodic solution are obtained. And the impulsive controllers are designed to make the pest populations stay at the refuge level. Some simulations are carried out to prove the results.

Stability of Singular and Time－Delay Measure Differential Large－Scale Systems with Impulse Effects

This paper is devoted to the investigation of stability for singular and time-delay measure differential large scale systems with impulsive solution.With the help of Drazin inverse,the variation of parameters formula of large scale singular systems containing measures and delays is obtained.Employing inequality methods and comparison theory,the stability properties of large scale systems are studied.

OSCILLATIONS OF FOURTH ORDER ODE WITH IMPULSES

Sufficient conditions to guarantee the oscillations of fourth order ODE with impulses are obtained. The importance of the impulsive effect on the oscillations of higher order differential equations is stressed.

OSCILLATIONS OF A CLASS OF HIGH-ORDER LINEAR ODE WITH IMPULSES

Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.