scholarly journals Stability conditions for infinite networks of nonlinear systems and their application for stabilization

Automatica ◽  
2020 ◽  
Vol 112 ◽  
pp. 108643 ◽  
Author(s):  
Sergey Dashkovskiy ◽  
Svyatoslav Pavlichkov
Keyword(s):  
Nonlinear Systems ◽  
Stability Conditions ◽  
Infinite Networks

Delay-Independent Stability Conditions for Some Classes of Nonlinear Systems

2014 ◽  
Vol 59 (8) ◽  
pp. 2209-2214 ◽  
Author(s):  
Alexander Yu. Aleksandrov ◽  
Guang-Da Hu ◽  
Alexey P. Zhabko
Keyword(s):  
Nonlinear Systems ◽  
Stability Conditions

SOS Stability Conditions for Nonlinear Systems Based on a Polynomial Fuzzy Lyapunov Function

2011 ◽  
Vol 44 (1) ◽  
pp. 12777-12782 ◽  
Author(s):  
Kevin Guelton ◽  
Noureddine Manamanni ◽  
Darius L. Koumba-Emianiwe ◽  
Cuong Duong Chinh
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Stability Conditions ◽  
Fuzzy Lyapunov Function

Absolute Stability of a Class of Singular Nonlinear Systems with Set-Valued Mappings

2014 ◽  
Vol 24 (01) ◽  
pp. 1550015 ◽  
Author(s):  
Gaoming Feng ◽  
Xingguo Tan
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Absolute Stability ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Set Valued Mappings ◽  
The Absolute

A class of singular nonlinear systems with set-valued mappings are studied in this paper. Criteria are given based on the Lyapunov function to check the absolute stability of the systems, then the results are extended to the time delay systems and the time delay systems with uncertainty. Three examples are simulated to show the effectiveness of the proposed stability conditions.

scholarly journals CHAOS SYNCHRONIZATION IN THE MULTIFEEDBACK MACKEY–GLASS MODEL

2005 ◽  
Vol 19 (23) ◽  
pp. 3613-3618 ◽  
Author(s):  
E. M. SHAHVERDIEV ◽  
R. A. NURIEV ◽  
L. H. HASHIMOVA ◽  
E. M. HUSEYNOVA ◽  
R. H. HASHIMOV
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Stability Conditions ◽  
Complete Synchronization ◽  
Glass Model ◽  
Existence And Stability

We investigate synchronization between two unidirectionally linearly coupled chaotic multifeedback Mackey–Glass systems and find the existence and stability conditions for complete synchronization. Numerical simulations fully support the theory. We also present generalization of the approach to the wider class of nonlinear systems.

scholarly journals Nonlinear small-gain theorems for input-to-state stability of infinite interconnections

2021 ◽  
Author(s):  
Andrii Mironchenko ◽  
Christoph Kawan ◽  
Jochen Glück
Keyword(s):  
Nonlinear Systems ◽  
Spectral Radius ◽  
Heterogeneous Networks ◽  
Infinite Dimension ◽  
Small Gain ◽  
Efficient Criteria ◽  
Infinite Networks

AbstractWe consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain condition. We show that for finite networks of nonlinear systems this condition is equivalent to the so-called strong small-gain condition of the gain operator (and thus our results extend available results for finite networks), and for infinite networks with a linear gain operator they correspond to the condition that the spectral radius of the gain operator is less than one. We provide efficient criteria for input-to-state stability of infinite networks with linear gains, governed by linear and homogeneous gain operators, respectively.

Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices

2021 ◽  
Vol 24 (3) ◽  
pp. 950-962
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Global Stability ◽  
Positive Feedback ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Stability Conditions ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Fractional Orders ◽  
Nonlinear Feedback Systems

Abstract The global stability of continuous-time fractional orders nonlinear feedback systems with positive linear parts and interval state matrices is investigated. New sufficient conditions for the global stability of this class of positive feedback nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple example.

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