scholarly journals Asymptotic Stability of the Golden-Section Control Law for Multi-Input and Multi-Output Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Duo-Qing Sun ◽  
Zhu-Mei Sun
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Golden Section ◽  
Stability Result ◽  
Least Square ◽  
Control Law ◽  
Phase System ◽  
Characteristic Model ◽  
Model Based ◽  
The Stability

This paper is concerned with the problem of the asymptotic stability of the characteristic model-based golden-section control law for multi-input and multi-output linear systems. First, by choosing a set of polynomial matrices of the objective function of the generalized least-square control, we prove that the control law of the generalized least square can become the characteristic model-based golden-section control law. Then, based on both the stability result of the generalized least-square control system and the stability theory of matrix polynomial, the asymptotic stability of the closed loop system for the characteristic model under the control of the golden-section control law is proved for minimum phase system.

scholarly journals Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 401-408 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Type Model ◽  
Stability Tests ◽  
Numerical Examples ◽  
Computer Methods ◽  
Discrete Linear Systems ◽  
Complex Functions ◽  
The Stability

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
Author(s):  
J. Klamka ◽  
A. Czornik ◽  
M. Niezabitowski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Arbitrary Switching ◽  
Mathematical Problems ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

scholarly journals Characteristic Modeling and Control of Servo Systems with Backlash and Friction

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Yifei Wu ◽  
Zhihong Wang ◽  
Yuanyuan Li ◽  
Wei Chen ◽  
Renhui Du ◽  
...  
Keyword(s):  
Golden Section ◽  
Dynamic Performance ◽  
Friction Model ◽  
Control Law ◽  
Mathematical Function ◽  
Servo Systems ◽  
Integral Control ◽  
Characteristic Model ◽  
Modeling And Control ◽  
And Control

A novel approach for modeling and control of servo systems with backlash and friction is proposed based on the characteristic model. Firstly, to deal with friction-induced nonlinearities, a smooth Stribeck friction model is introduced. The backlash is modeled by a continuous and derivable mathematical function. Secondly, a characteristic model in the form of a second-order slowly time-varying difference equation is established and verified by simulations. Thirdly, a composite controller including the golden-section adaptive control law and the integral control law is designed and the stability of the closed-loop system is analyzed. The simulation and experimental results show that the proposed control scheme is effective and can improve the steady-state precision and the dynamic performance of the servo system with backlash and friction.

Global Asymptotic Stability of Stochastic Fuzzy Cellular Neural Networks with Time-Varying Delays

2010 ◽  
Vol 139-141 ◽  
pp. 1714-1717
Author(s):  
Wen Guang Luo ◽  
Yong Hua Liu ◽  
Hong Li Lan
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
The Stability ◽  
Delay Dependent

In this paper, the problem of global asymptotic stability in the mean square for stochastic fuzzy cellular neural networks (SFCNN) with time-varying delays is investigated. By constructing a newly proposed Lyapunov-Krasovskii function (LKF) and using Ito’s stochastic stability theory, a novel delay-dependent stability criterion is derived. The obtained stability result is helpful to design the stability of fuzzy cellular neural networks (FCNN) with time-varying delays when stochastic noise is taken into consideration. Since it is presented in terms of a linear matrix inequality (LMI), the sufficient condition is easy to be checked efficiently by utilizing some standard numerical packages such as the LMI Control Toolbox in Matlab. Finally, an illustrate example is given to verify the feasibility and usefulness of the proposed result.

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