scholarly journals Stability Analysis of 2D Discrete Linear System Described by the Fornasini-Marchesini Second Model with Actuator Saturation

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Richa Negi ◽  
Haranath Kar ◽  
Shubhi Purwar
Keyword(s):  
Stability Analysis ◽  
Linear System ◽  
State Space ◽  
Linear Systems ◽  
Actuator Saturation ◽  
Discrete Systems ◽  
Stability Conditions ◽  
Numerical Examples ◽  
Discrete Linear Systems ◽  
2D Discrete Systems

This paper proposes a novel antiwindup controller for 2D discrete linear systems with saturating controls in Fornasini-Marchesini second local state space (FMSLSS) setting. A Lyapunov-based method to design an antiwindup gain of 2D discrete systems with saturating controls is established. Stability conditions allowing the design of antiwindup loops, in both local and global contexts have been derived. Numerical examples are provided to illustrate the applicability of the proposed method.

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.

scholarly journals An iterative frequency-sweeping approach for stability analysis of linear systems with multiple delays

2017 ◽  
Vol 36 (2) ◽  
pp. 379-398
Author(s):  
Xu-Guang Li ◽  
Silviu-Iulian Niculescu ◽  
Arben Çela
Keyword(s):  
Stability Analysis ◽  
Asymptotic Behaviour ◽  
Linear Systems ◽  
Invariance Property ◽  
Multiple Delays ◽  
Numerical Examples ◽  
The Stability ◽  
Imaginary Roots ◽  
Frequency Sweeping

AbstractIn this article, we study the stability of linear systems with multiple (incommensurate) delays, by extending a recently proposed frequency-sweeping approach. First, we consider the case where only one delay parameter is free while the others are fixed. The complete stability w.r.t. the free delay parameter can be systematically investigated by proving an appropriate invariance property. Next, we propose an iterative frequency-sweeping approach to study the stability under any given multiple delays. Moreover, we may effectively analyse the asymptotic behaviour of the critical imaginary roots (if any) w.r.t. each delay parameter, which provides a possibility for stabilizing the system through adjusting the delay parameters. The approach is simple (graphical test) and can be applied systematically to the stability analysis of linear systems including multiple delays. A deeper discussion on its implementation is also proposed. Finally, various numerical examples complete the presentation.

scholarly journals MITTAG-LEFFLER STABILITY ANALYSIS OF TEMPERED FRACTIONAL NEURAL NETWORKS WITH SHORT MEMORY AND VARIABLE-ORDER

Fractals ◽  
2021 ◽  
pp. 2140029
Author(s):  
CHUAN-YUN GU ◽  
FENG-XIA ZHENG ◽  
BABAK SHIRI
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Stability Analysis ◽  
Fixed Point Theorem ◽  
Banach Fixed Point Theorem ◽  
Stability Conditions ◽  
Variable Order ◽  
Numerical Examples ◽  
Short Memory ◽  
Theoretical Results

A class of tempered fractional neural networks is proposed in this paper. Stability conditions for tempered fractional neural networks are provided by using Banach fixed point theorem. Attractivity and Mittag-Leffler stability are given. In order to show the efficiency and convenience of the method used, tempered fractional neural networks with and without delay are discussed, respectively. Furthermore, short memory and variable-order tempered fractional neural networks are proposed under the global conditions. Finally, two numerical examples are used to demonstrate the theoretical results.

scholarly journals Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuangong Sun ◽  
Zhaorong Wu ◽  
Fanwei Meng
Keyword(s):  
Stability Analysis ◽  
Complex Systems ◽  
Linear Systems ◽  
Algebraic Structure ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.

scholarly journals Perfect observer resistant to the changes of dynamics of the standard linear system

2017 ◽  
Vol 65 (3) ◽  
pp. 313-316
Author(s):  
M. A. Sławiński
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Numerical Examples ◽  
Standard Linear ◽  
Time Linear

AbstractThe article presents a class of perfect observers for standard continuous-time linear systems. Observers are resistant to significant changes in the dynamics of the system. The value of poles of the system can be unlimited as long as their number does not change and the conditions presented in this article are satisfied. There are presented numerical examples and simulations results.

Applications and Techniques of Inners to Stability, Analysis, and Synthesis

1975 ◽  
Vol 97 (3) ◽  
pp. 249-256 ◽  
Author(s):  
M. R. Clark
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Discrete Systems ◽  
Analysis Method ◽  
Analysis And Synthesis

Recently, E. I. Jury has developed an analysis method for linear systems based on the concept of Inners. His approach uniformly treats both continuous and discrete systems while being computationally simpler than previous techniques. The aim of this paper is to introduce and explain some of the more general applications of the Inners method to problems in stability, analysis, and synthesis of linear systems.

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