Input-to-state stability of stochastic nonlinear system with delayed impulses
1School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.
Abstract:
Stochastic input-to-state stability (SISS) of the stochastic nonlinear system has received extensive research. This paper aimed to investigate SISS of the stochastic nonlinear system with delayed impulses. First, when all subsystems were stable, using the average impulsive interval method and Lyapunov approach, some theoretical conditions ensuring SISS of the considered system were established. The SISS characteristic of the argumented system with both stable and unstable subsystems was also discussed, then the stochastic nonlinear system with multiple delayed impulse jumps was considered and SISS property was explored. Additionally, it should be noted that the Lyapunov rate coefficient considered in this paper is positively time-varying. Finally, several numerical examples confirmed validity of theoretical results.
Related Concept Videos
Transient and Steady-state Response
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
First Order Systems
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Second Order systems II
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...


