scholarly journals Analysis of stability problems via matrix Lyapunov functions

1990 ◽  
Vol 3 (4) ◽  
pp. 209-226 ◽  
Author(s):  
Anatoly A. Martynyuk
Keyword(s):  
Lyapunov Functions ◽  
Systems Of Nonlinear Equations ◽  
Matrix Functions ◽  
Singularly Perturbed Systems ◽  
Two Component System ◽  
Two Component ◽  
Lyapunov Matrix ◽  
Analysis Of Stability ◽  
The Stability ◽  
The Given

The stability of nonlinear systems is analyzed by the direct Lyapunov's method in terms of Lyapunov matrix functions. The given paper surveys the main theorems on stability, asymptotic stability and nonstability. They are applied to systems of nonlinear equations, singularly-perturbed systems and hybrid systems. The results are demonstrated by an example of a two-component system.

scholarly journals On effective criterion of stability of partial indices for matrix polynomials

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200012
Author(s):  
N. V. Adukova ◽  
V. M. Adukov
Keyword(s):  
Small Perturbation ◽  
Stability Criterion ◽  
Matrix Function ◽  
Toeplitz Matrices ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Partial Indices ◽  
The Stability ◽  
The Given

In the work, we obtain an effective criterion of the stability of the partial indices for matrix polynomials under an arbitrary sufficiently small perturbation. Verification of the stability is reduced to calculation of the ranks for two explicitly defined Toeplitz matrices. Furthermore, we define a notion of the stability of the partial indices in the given class of matrix functions. This means that we will consider an allowable small perturbation such that a perturbed matrix function belong to the same class as the original one. We prove that in the class of matrix polynomials the Gohberg–Krein–Bojarsky criterion is preserved, i.e. new stability cases do not arise. Our proof of the stability criterion in this class does not use the Gohberg–Krein–Bojarsky theorem.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

The role of PhoP/PhoQ two component system in regulating stress adaptation in Cronobacter sakazakii

2021 ◽  
pp. 103851
Author(s):  
Yan Ma ◽  
Yingying Zhang ◽  
Ke Chen ◽  
Lingzhu Zhang ◽  
Yibei Zhang ◽  
...  
Keyword(s):  
Stress Adaptation ◽  
Cronobacter Sakazakii ◽  
Two Component System ◽  
Component System ◽  
Two Component

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

Sign in / Sign up

Export Citation Format

Share Document