Observer‐based finite‐time H_∞ control of Itô‐type stochastic nonlinear systems

Abstract

This paper investigates the finite‐time H∞$$ {H}_{\infty } $$ control of Itô‐type stochastic nonlinear systems. Considering the transient performance and anti‐interference ability within a given limited time interval, the control strategy of stochastic nonlinear systems is researched. A new sufficient condition for mean‐square finite‐time boundedness for stochastic nonlinear system is developed. Due to the state components are not available, a state observer is designed. Based on the estimated state, an H∞$$ {H}_{\infty } $$ controller is proposed and Linear Matrix Inequality (LMI) conditions are given, which not only guarantee the mean‐square finite‐time boundedness but also satisfy the corresponding H∞$$ {H}_{\infty } $$ performance. Finally, two examples are given to demonstrate the effectiveness of the results.

Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities

“…Remark 8. We can note that conditions ( 26), ( 29), (37), and ( 41) are not strict LMIs; however, once we fix the parameters α and β, the conditions can be turned into LMI-based feasibility problems. Therefore, the feasibility of the conditions stated in Theorems 2 and 4 can be turned into the following feasibility problems with the fixed parameters α and β, respectively: min (ρ 2 + γ 2 ) s.t.…”

“…To weaken the effect of external disturbances, H ∞ control has emerged. Recently, many scholars have carried out plenty of research on finite-time H ∞ control [35][36][37][38][39][40][41]. Specifically, ref.…”

“…On the other hand, due to the constraints of measurement technology and measurement costs, the system state information is frequently challenging to measure directly. In tackling this challenge, many meaningful results of finite-time H ∞ observer-based controller designing schemes have been successfully attained; see [37][38][39][40][41] and references therein.…”

Robust H∞ sliding mode control scheme for uncertain fractional stochastic systems: Nonlinear analysis and design

“…In [5], the fractional infinitesimal operator has been proposed for linear fractional stochastic dynamics, and a sliding mode control (SMC) scheme has been introduced. Nonlinear stochastic systems have also been richly investigated formerly [6][7][8]; however, there are few works addressing fractional nonlinear stochastic systems driven by fBm.…”

Hidden Markov model‐based asynchronous exponential stabilization for stochastic Markovian jump systems with incomplete controller mode information

“…Naturally, it is highly desirable to connect MJSs with the Brownian motion, holding great promise for theoretical novelties and practical applications. In recent years, a lot of works have been conducted to yield rich results on MJSs with It ô motions [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In more detail, [10] addressed the stochastic stability problem for semi-MJSs with It ô-type nonlinearity.…”