Mean‐square strong stability and stabilization of discrete‐time stochastic systems with multiplicative noises

Abstract

This article investigates the mean-square strong stability and stabilization of a discrete-time stochastic system corrupted by multiplicative noises. First, the definition of the mean-square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS-strong stability are derived. Moreover, the relationship between MS-strong stability and MS-stability is given. Second, some necessary and sufficient conditions of the MS-strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.

Event‐triggered control of Itô stochastic nonlinear delayed systems with state quantization

“…ẍ(t) + (a + b Ḃ(t)) ̇x(t) + e Ḃ(t) ̇x(t) + x(t) + dx(t − 𝜏 1 ) + c sin x(t) = u(t), (30) where x(t) is the displacement, Ḃ(t) is the white noise, u(t) is the control input, constant a is the coefficient of the linear damping, constants b, e are the forcing intensity, and c, d are deterministic coefficients. Based on system (30), taking x 1 (t) = x(t), x 2 (t) = ̇x(t), we can rewrite the system (30) as the system (1) with (2) where…”

“…Stochastic perturbations have become a common phenomenon frequently occurring in real-world systems due to environmental noise and human disturbances. 1,2 The dynamic characteristics of industrial processes can be more accurately reflected as the effects of randomization are accounted for in the system. It is well known that many scholars have widely examined Itô stochastic systems in various areas such as bioengineering, economics, and mechanical systems.…”

“…Stochastic perturbations have become a common phenomenon frequently occurring in real‐world systems due to environmental noise and human disturbances 1,2 . The dynamic characteristics of industrial processes can be more accurately reflected as the effects of randomization are accounted for in the system.…”

Local H∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions

“…(3) The extended stabilization conditions for H∞ performance are obtained by polynomial technology. As q increases, conservatism of obtained conditions will reduce, and the proposed method can be generalized to handle other cases, such as output feedback controller design [5], finite-time annular domain stability [29],mean-square strong stability [30].…”