Razumikhin stability theorems for a general class of stochastic impulsive switched time-delay systems

• This paper studies stability of a general class of impulsive switched systems under time delays and random disturbances using multiple Lyapunov functions and fixed dwell-time. In the studied system model, the impulses and switches are allowed to occur asynchronously. As a result, the switching may occur in the impulsive intervals and the impulses can occur in the switching intervals, which have great effects on system stability. Since the switches do not bring about the change of the system state, we study two cases in terms of the impulses, ie, the stable continuous dynamics case and the stable impulsive dynamics case. According to multiple Lyapunov-Razumikhin functions and the fixed dwell-time, Razumikhin-type stability conditions are established. Finally, the obtained results are illustrated via a numerical example from the synchronization problem of chaotic systems.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

fixed dwell-time

impulsive switched systems

Lyapunov-Razumikhin function

stochastic stability

stochastic systems

time-delay systems

Publication and Content Type

ref (subject category)

art (subject category)