Abstract
In this paper, the problem of stochastic finite-time stabilization is investigated for stochastic delay interval systems. A nonlinear state feedback controller with input-to-state delay is introduced. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions on stochastic finite-time stabilization are derived for closed-loop stochastic delay interval systems using the I t o ^ ’s differential formula. Suitable nonlinear state feedback controllers can be designed in terms of linear matrix inequalities. The obtained results are finally applied to an energy-storing electrical circuit to illustrate the effectiveness of the proposed method.
Highlights
The feedback of real-world systems to external signals is not instantaneous as it is usually affected by a certain time delay
This paper aims to investigate the finite-time stabilization problem of stochastic delay interval systems
That means the energy-storing electrical circuit with time delay and stochastic disturbance is not SFTS according to the terms of Definition 2, which is illustrated by the phase planes in Figures 4 and 5
Summary
The feedback of real-world systems to external signals is not instantaneous as it is usually affected by a certain time delay. A lot of investigations on energy-storing electrical circuits have been published, e.g., finite-time control [36], stability [37], and passivity [38,39]. In the existing results related to energy-storing electrical circuits, the stochastic disturbance is not considered, and the values of electronic components are exact. This is almost impossible in practical energy-storing electrical circuits. This paper aims to investigate the finite-time stabilization problem of stochastic delay interval systems. To tackle this problem, a nonlinear delay-feedback controller was used.
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