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Stability and Stabilization of Stochastic Systems with Multiplicative Noise
Huiying Sun,Meng Li,Weihai Zhang 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.2
In this paper, stability and stabilization of linear stochastic time-invariant systems are studied based on spectrum technique. Firstly, the relationship among mean square exponential stability, asymptotical mean square stability, second-order moment exponential stability and the spectral location of the systems is revealed with the help of a spectrum operator LA,C. Then, we focus on almost sure exponential stability and stochastic stabilization. A criterion on almost sure exponential stability based on spectrum technique is obtained. Sufficient conditions for mean square exponentially stability and asymptotic mean square stability are given via linear matrix inequality approach and some numerical examples to illustrate the effectiveness of our results are presented.
An LMI Approach to Exponential Stabilization of Uncertain Time-Delay Systems
Hyoun-Chul Choi,Hyungbo Shim,Jin Heon Seo 제어로봇시스템학회 2008 제어로봇시스템학회 국제학술대회 논문집 Vol.2008 No.10
This paper presents a new, sufficient condition for exponential stabilization of uncertain systems with statedelays. By using a new Lyapunov function, the condition is obtained to be delay-dependent and represented in terms of linear matrix inequalities. Unlike some existing results on exponential stability and stabilization problems of timedelay systems, our condition involves information on the degree of exponential decay rates and therefore can suggest an achievable degree of speed of stabilization. Numerical examples are presented to show the effectiveness of the proposed method.
Qiuqiu Fan,Zhao-Yan Li,Longsuo Li 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.2
This article aims to explore the stability and stabilization of a more practical class of stochastic neutraltype Markovian jump time-delay systems (SNMJTDSs) with two delays in the derivative. First, a less restrictive condition is imposed on the associated difference operator to ensure its stability. Second, by constructing novel Lyapunov-Krasovskii functionals, sufficient conditions for exponential stability (in the sense of mean square and almost sure) are established. Then, the SNMJTDS is stabilized by designing a delayed feedback controller. Finally, the less conservativeness of the proposed stability criterion and the validity of the designed controller are checked through two examples.
STABILITY OF PARTIALLY PEXIDERIZED EXPONENTIAL-RADICAL FUNCTIONAL EQUATION
Choi, Chang-Kwon Korean Mathematical Society 2021 대한수학회보 Vol.58 No.2
Let ℝ be the set of real numbers, f, g : ℝ → ℝ and ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.
입력 지연을 갖는 이산시간 선형 시스템을 위한 예측기 피드백의 지수적 안정성
최준형,Choi, Joon-Young 제어로봇시스템학회 2013 제어·로봇·시스템학회 논문지 Vol.19 No.7
We consider discrete-time LTI (Linear Time-Invariant) systems with constant input delays. The input delay is modeled by a first-order PdE (Partial difference Equation) and a backstepping transformation is employed to design a predictor feedback controller. The backstepping approach results in the construction of an explicit Lyapunov function, with which we prove the exponential stability of the closed-loop system formed by the predictor feedback. The numerical example demonstrates the design of the predictor feedback controller, and illustrates the validity of the exponential stability.
Qian-qian Mu,Fei Long,Qi-xiang Wang,Lang Zhang,Li-po Mo 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1
In this paper, the almost surely globally asymptotical stability and the almost surely exponential stability for dual switching continuous-time nonlinear system are investigated by using the probability analysis method and stochastic Multi-Lyapunov function, respectively. Different from the previous research results, it is the first time that dual switching continuous-time nonlinear system is used as a study object to investigate its switching stability. Then, the probability analysis method is used to overcome the deficiency that the ergodicity no longer holds due to the variable transition rate of Markov process. Some sufficient conditions for the globally asymptomatic stability almost surely and the almost surely exponential stability of dual switching continuous-time nonlinear system are given under the pre-designed deterministic switching strategy. Finally, two numerical examples are provided to verify the effectiveness of the proposed approach.
UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS
Sang Il Choi,구윤회 한국수학교육학회 2016 純粹 및 應用數學 Vol.23 No.1
This paper shows that the solutions to the perturbed differential system y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds+h(t,y(t)) have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part \int_{t_0}^tg(s,y(s),Ty(s))ds, h(t,y(t)), and on the fundamental matrix of the unperturbed system y'=f(t,y).
Adaptive Fault-tolerant Control of Platoons With Prescribed Tracking Performance
Guanglei Zhao,Gaoge Dai,Hailong Cui,Bingkang Peng 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.7
This article investigates a heterogeneous vehicular platoon control problem, in which prescribed tracking performance can be achieved, it is assumed that the vehicle subjects to asymmetric nonlinear actuator saturation, dead-zone nonlinearity and actuator faults. Based on improved exponential spacing policy, an adaptive fault-tolerant sliding-mode control scheme is proposed to guarantee individual vehicle stability, string stability and traffic flow stability. The hypothesis that the spacing errors at initial time are zero is removed by employing the novel exponential spacing policy. Furthermore, to attenuate the harmful effects of actuator faults, saturation and dead-zone nonlinearity, a compensation system based on radial basis neural network (RBFNN) is established. Finally, the effectiveness of the proposed control scheme is verified by simulation results.
입력 지연을 갖는 이산시간 선형 시스템을 위한 예측기 피드백의 지수적 안정성
최준영(Joon-Young Choi) 제어로봇시스템학회 2013 제어·로봇·시스템학회 논문지 Vol.19 No.7
We consider discrete-time LTI (Linear Time-Invariant) systems with constant input delays. The input delay is modeled by a first-order PdE (Partial difference Equation) and a backstepping transformation is employed to design a predictor feedback controller. The backstepping approach results in the construction of an explicit Lyapunov function, with which we prove the exponential stability of the closed-loop system formed by the predictor feedback. The numerical example demonstrates the design of the predictor feedback controller, and illustrates the validity of the exponential stability.
Transverse Vibration Control of Axially Moving Web Systems by Regulation of Axial Tension
Quoc Chi Nguyen,Quang Hieu Ngo,Keum-Shik Hong 제어로봇시스템학회 2010 제어로봇시스템학회 국제학술대회 논문집 Vol.2010 No.10
In this paper, an active control scheme that suppresses transverse vibrations and regulates axial speed so as to track a desired profile for an axially moving web system is investigated. The spatially varying tension and the time-varying axial speed of the axially moving web are considered. The system dynamics includes the equations of motion of the moving web and the velocity dynamics of the drive rollers at boundaries of the web span. The two roller motors provide control torque inputs for the control system. The principle of the vibration control strategy is the regulation of the axial tension by a designed profile according to which the vibration energy of the moving web decays. The designed profile for the axial tension is generated by using vibration analysis based on the total mechanical energy of the axially moving web system. Lyapunov method is employed to derive the model-based torque control laws ensuring that the transverse vibration and the speed tracking error converge to zero exponentially. The effectiveness of the proposed control scheme is demonstrated via numerical simulations.