On Stability and Stabilization of Mechanical Structures Under Nonlinear Time-Varying Perturbations

1991 ◽  
Vol 58 (2) ◽  
pp. 527-535
Author(s):  
Chun-Liang Lin ◽  
Bor-Sen Chen ◽  
Fei-Bin Hsiao
Keyword(s):  
Asymptotic Stability ◽  
State Transition ◽  
Time Varying ◽  
Bibo Stability ◽  
Perturbed System ◽  
System A ◽  
Stability And Stabilization ◽  
Norm Bound ◽  
Bounded Input ◽  
Modal Space

Asymptotic stability and bounded-input, bounded-output (BIBO) stability of a class of underdamped mechanical structures with nonlinear time-varying perturbations are studied. An upper norm-bound of the state transition matrix of a normal mode system is derived. We provide a sufficient condition which guarantees both asymptotic stability and BIBO stability for the perturbed system. A straightforward extension to a robust modal-space control is also briefly introduced. Finally, simple illustrative examples are presented for demonstrating the applications of our results

scholarly journals BIBO Stability Analysis for Delay Switched Systems with Nonlinear Perturbation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jincheng Wei ◽  
Peng Shi ◽  
Hamid Reza Karimi ◽  
Bo Wang
Keyword(s):  
Numerical Simulation ◽  
Switched Systems ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Functional Theory ◽  
Bibo Stability ◽  
Delay Dependent ◽  
Bounded Input

The problem of bounded-input bounded-output (BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper.

scholarly journals STABILITY AND STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS

2017 ◽  
Vol 20 (1) ◽  
pp. 61-70
Author(s):  
P. Sattayatham ◽  
R. Saelim ◽  
S. Sujitjorn
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Feedback Controllers ◽  
Nonlinear Dynamical ◽  
System A ◽  
Continuous Feedback ◽  
Stability And Stabilization ◽  
The Stability

Exponential and asymptotic stability for a class of nonlinear dynamical systems with uncertainties is investigated.  Based on the stability of the nominal system, a class of bounded continuous feedback controllers is constructed.  By such a class of controllers, the results guarantee exponential and asymptotic stability of uncertain nonlinear dynamical system.  A numerical example is also given to demonstrate the use of the main result.

Switching Design for the Asymptotic Stability and Stabilization of Nonlinear Uncertain Stochastic Discrete-time Systems

2013 ◽  
Vol 14 (1) ◽  
pp. 33-44
Author(s):  
Grienggrai Rajchakit
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Discrete Time Delay ◽  
Stability And Stabilization

Abstract This paper is concerned with asymptotic stability and stabilization of nonlinear uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability and stabilization for the nonlinear uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

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