scholarly journals Some Contributions to Stochastic Asymptotic Stability and Boundedness via Multiple Lyapunov Functions

2001 ◽  
Vol 260 (2) ◽  
pp. 325-340 ◽  
Author(s):  
Xuerong Mao
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Stochastic Asymptotic Stability

Stability of a class of nonlinear fractional order impulsive switched systems

2016 ◽  
Vol 39 (5) ◽  
pp. 781-790 ◽  
Author(s):  
Guopei Chen ◽  
Ying Yang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Unstable Subsystems ◽  
Impulsive Switched Systems ◽  
The Stability ◽  
Work First ◽  
Periodic Switching

This paper considers the asymptotic stability of a class of nonlinear fractional order impulsive switched systems by extending the result of existing work. First, a criterion is given to verify the stability of systems by using the Mittag–Leffler function and fractional order multiple Lyapunov functions. Second, by combining the methods of minimum dwell time with fractional order multiple Lyapunov functions, another sufficient condition for the stability of systems is given. Third, by using a periodic switching technique, a switching signal is designed to ensure the asymptotic stability of a system with both stable and unstable subsystems. Finally, two numerical examples are provided to illustrate the theoretical results.

Recursive Lyapunov Functions

1989 ◽  
Vol 111 (4) ◽  
pp. 641-645 ◽  
Author(s):  
Andrzej Olas
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Performance Measures ◽  
Lyapunov Functions ◽  
Stability Problem ◽  
Autonomous Systems ◽  
Sequence Of Functions

The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

Stability of a Class of Piezoelectric State-Switching Methods

2000 ◽  
Author(s):  
Andrew J. Kurdila ◽  
William W. Clark ◽  
Weijian Wang ◽  
Dwayne E. McDaniel
Keyword(s):  
Lyapunov Functions ◽  
Closed Loop ◽  
Control Strategies ◽  
Short Circuit ◽  
Open Circuit ◽  
Hybrid Dynamical Systems ◽  
Multiple Lyapunov Functions ◽  
Control Laws ◽  
State Switching ◽  
The Stability

Abstract Experimental and anecdotal evidences have shown that state-switched control strategies for piezoelectric actuators can be advantageous. However, most discussions of the stability of these systems has relied on heuristic, or physically motivated, arguments. In this paper, we show that recent open-circuit/short-circuit state-switching control laws can be viewed as hybrid dynamical systems of Witsenhausen type. Within this framework, the closed-loop stability of OC/SC switching is rigorously established using the method of multiple Lyapunov functions.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

Exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay

2018 ◽  
Vol 41 (2) ◽  
pp. 350-365 ◽  
Author(s):  
Xin Zhang ◽  
Huashan Liu ◽  
Yiyuan Zheng ◽  
Yuqing Sun ◽  
Wuneng Zhou ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Stochastic Systems ◽  
Transition Probabilities ◽  
Time Varying ◽  
Analysis Method ◽  
Multiple Lyapunov Functions ◽  
Time Varying Delay ◽  
Neutral Stochastic Systems ◽  
Varying Delay

This paper discusses the problem of exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay. Based on non-convolution type multiple Lyapunov functions and stochastic analysis method, we obtain the conditions which are independent to any decay rate of the exponential stability for uncertain transition probabilities neutral stochastic systems with time-varying delay. Finally, two examples are presented to illustrate the effectiveness and potential of the proposed results.

Multiple Lyapunov Functions for Adaptive Neural Tracking Control of Switched Nonlinear Nonlower-Triangular Systems

2020 ◽  
Vol 50 (5) ◽  
pp. 1877-1886 ◽  
Author(s):  
Ben Niu ◽  
Yanjun Liu ◽  
Wanlu Zhou ◽  
Haitao Li ◽  
Peiyong Duan ◽  
...  
Keyword(s):  
Tracking Control ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Triangular Systems
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