The theorem of the stability of nonlinear nonautonomous systems under the frequently-acting perturbation —Liapunov's indirect method

1991 ◽  
Vol 12 (7) ◽  
pp. 717-725
Author(s):  
Zhang Shu-shun ◽  
Shang Da-zhang
Keyword(s):  
Indirect Method ◽  
Nonautonomous Systems ◽  
The Stability

scholarly journals Stability and Convergence Analysis of Direct Adaptive Inverse Control

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Shafiq ◽  
Muhammad A. Shafiq ◽  
Hassan A. Yousef
Keyword(s):  
Computer Simulation ◽  
Convergence Analysis ◽  
Indirect Method ◽  
Stability And Convergence ◽  
Adaptive Inverse Control ◽  
Inverse Control ◽  
Simulation Results ◽  
The Stability ◽  
Feed Forward Controller ◽  
Physical Plants

In adaptive inverse control (AIC), adaptive inverse of the plant is used as a feed-forward controller. Majority of AIC schemes estimate controller parameters using the indirect method. Direct adaptive inverse control (DAIC) alleviates the adhocism in adaptive loop. In this paper, we discuss the stability and convergence of DAIC algorithm. The computer simulation results are presented to demonstrate the performance of the DAIC. Laboratory scale experimental results are included in the paper to study the efficiency of DAIC for physical plants.

scholarly journals On the stability of nonautonomous systems

Automatica ◽  
2003 ◽  
Vol 39 (1) ◽  
pp. 167-171 ◽  
Author(s):  
A. Iggidr ◽  
G. Sallet
Keyword(s):  
Nonautonomous Systems ◽  
The Stability

scholarly journals Stability and Controllability of Nonlinear Systems

2020 ◽  
pp. 51-60
Author(s):  
S. T. Cotterell ◽  
I. Davies ◽  
L. C. Abraham
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Equilibrium Solution ◽  
Indirect Method ◽  
Real Life ◽  
Linearization Method ◽  
Controlled System ◽  
The Stability ◽  
Theoretical Results

This paper is aimed at establishing new stability and controllability results for nonlinear systems. The approach is to use the Lyapunov indirect method to obtain the stability of the equilibrium solution of the uncontrolled nonlinear system by applying the Jacobi’s linearization method and the controllability of the controlled system obtained by the rank criterion for properness. Example is given with a real-life application to illustrate the effectiveness of the theoretical results.

scholarly journals On the Stability of Some Discrete Fractional Nonautonomous Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Fahd Jarad ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Kübra Biçen
Keyword(s):  
Asymptotic Stability ◽  
Global Stability ◽  
Direct Method ◽  
Uniform Stability ◽  
Lyapunov Direct Method ◽  
Uniform Asymptotic Stability ◽  
Fractional Difference ◽  
Nonautonomous Systems ◽  
The Stability

Using the Lyapunov direct method, the stability of discrete nonautonomous systems within the frame of the Caputo fractional difference is studied. The conditions for uniform stability, uniform asymptotic stability, and uniform global stability are discussed.

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