scholarly journals Stability analysis in terms of two measures for dynamic systems on time scales

1993 ◽  
Vol 6 (4) ◽  
pp. 325-344 ◽  
Author(s):  
Billûr Kaymakçalan
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov’S Second Method ◽  
Two Measures ◽  
Set Up ◽  
Stability Results ◽  
Stability Concepts ◽  
Single Set

Using the theory of Lyapunov's second method developed earlier for time scales, we extend our stability results to two measures which give rise to unification of several stability concepts in a single set up.

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

scholarly journals Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Kexue Zhang ◽  
Xinzhi Liu
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Impulsive Systems ◽  
Uniform Asymptotic Stability ◽  
Stability And Instability ◽  
Special Cases ◽  
Two Measures

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results.

scholarly journals Finite-Time Stability Analysis: A Tutorial Survey

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Honglei Xu
Keyword(s):  
Stability Analysis ◽  
Finite Time ◽  
Linear Time ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Systems ◽  
Stability And Stabilization ◽  
Dynamical System Models ◽  
Stability Results ◽  
Stability Concepts

In the past decades, there has been a growing research interest in the field of finite-time stability and stabilization. This paper aims to provide a self-contained tutorial review in the field. After a brief introduction to notations and two distinct finite-time stability concepts, dynamical system models, particularly in the form of linear time-varying systems and impulsive linear systems, are studied. The finite-time stability analysis in a quantitative sense is reviewed, and a variety of stability results including state transition matrix conditions, the piecewise continuous Lyapunov-like function theory, and the converse Lyapunov-like theorem are investigated. Then, robustness and time delay issues are studied. Finally, fundamental finite-time stability results in a qualitative sense are briefly reviewed.

NEURAL MODELING AND CONTROL OF DYNAMIC SYSTEMS WITH HYSTERESIS

2007 ◽  
Vol 31 (1) ◽  
pp. 127-141
Author(s):  
Yonghong Tan ◽  
Xinlong Zhao
Keyword(s):  
Dynamic Systems ◽  
Control Strategy ◽  
Neural Modeling ◽  
Modeling And Control ◽  
Control Scheme ◽  
The Neural Networks ◽  
Adaptive Control Strategy ◽  
Set Up ◽  
Modeling Strategy ◽  
And Control

A hysteretic operator is proposed to set up an expanded input space so as to transform the multi-valued mapping of hysteresis to a one-to-one mapping so that the neural networks can be applied to model of the behavior of hysteresis. Based on the proposed neural modeling strategy for hysteresis, a pseudo control scheme is developed to handle the control of nonlinear dynamic systems with hysteresis. A neural estimator is constructed to predict the system residual so that it avoids constructing the inverse model of hysteresis. Thus, the control strategy can be used for the case where the output of hysteresis is unmeasurable directly. Then, the corresponding adaptive control strategy is presented. The application of the novel modeling approach to hysteresis in a piezoelectric actuator is illustrated. Then a numerical example of using the proposed control strategy for a nonlinear system with hysteresis is presented.

Switched Dynamic Systems with Logic Switching and Its Stability Analysis

2021 ◽  
Vol 59 (2) ◽  
pp. 1188-1217
Author(s):  
Tao Sun ◽  
Xudong Zhao ◽  
Xi-Ming Sun
Keyword(s):  
Stability Analysis ◽  
Dynamic Systems
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