On practical stability of perturbed differential systems

On Stability of Nonlinear Differential System Via Cone-Perturbing Laipunov Function Method.

“…From the condition we obtain the differential inequality Applying the comparison Theorem of [7] , yields To prove that It must be show that…”

“…From the condition and applying the comparison Theorem [7 ] it yields From (5.3) at (5.8) From the condition and (5.6) , at (5.9) From (5.5),(5.8) and(5.9), we get From (5.2) ,we get (5.10) Then from the condition ,(5.4) , (5.6) and (5.10), we get at which leads to a contradiction ,then it must be holds ,provided that Therefore the zero solution of (1.1) is practically equistable.…”

Practical stability domai analysis of a class of dynamical system

“…Consequently, practical stability attracts much attention since it was fist introduced in [1]. For standard state-space systems, [2][3][4][5] presented a systematic study of the theory of practical stability and collected most of valuable results; but, there are few results about estimates of practical stability domain in existed paper. The concept of practical stability and the domain of practical stability [6], which is based on the works of Chetayev, Moiseyev, and Lefschetz [3],is more useful.…”

On Stability of Nonlinear Differential System via Cone-Perturbing Liapunov Function Method

“…The following definitions [6] will be needed in the sequal. , , x t t x is the maximal solution of (1.1).…”

“…The authors in [3] discussed some stability of system of ordinary differential equations, and in [4] [5] the authors discussed totally and totally φ 0 -stability of system of ordinary differential Equations (1.1) using Liapunov function method that was played essential role for determine stability of system of differential equations. In [6] the authors discussed practically stability for system of functional differential equations.…”