Browsing by Subject "Lyapunov function"

Now showing 1 - 6 of 6

Access status: Open Access ,
Dynamic system with random structure for modeling security and risk management in cyberspace
(Wydawnictwa AGH, 2019) Džalladova, Ìrada Agaêvna; Růžičková, Miroslava
We deal with the investigation of $L_{2}$-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for $L_{2}$-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.
Access status: Restricted ,
Metoda wyznaczania obszaru przyciągania punktu równowagi w układach nieliniowych z liniowym sprzężeniem zwrotnym od stanu
(Data obrony: 2012-05-30) Drochliński, Paweł
Wydział Elektrotechniki, Automatyki, Informatyki i Elektroniki
Access status: Open Access ,
On potential kernels associated with random dynamical systems
(2015) Hmissi, Mohamed; Mokchaha-Hmissi, Farida Chedly; Hmissi, Aya
Let $(\theta,\varphi)$ be a continuous random dynamical system defined on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and taking values on a locally compact Hausdorff space $E$. The associated potential kernel $V$ is given by $Vf(\omega ,x)= \int\limits_{0}^{\infty} f(\theta_{t}\omega,\varphi(t,\omega)x)dt, \quad \omega \in \Omega, x\in E.$ In this paper, we prove the equivalence of the following statements: 1. The potential kernel of $(\theta,\varphi)$ is proper, i.e. $Vf$ is $x$-continuous for each bounded, $x$-continuous function $f$ with uniformly random compact support. 2. $(\theta,\varphi)$ has a global Lyapunov function, i.e. a function $L:\Omega\times E \rightarrow (0,\infty)$ which is $x$-continuous and $L(\theta_t\omega, \varphi(t,\omega)x)\downarrow 0$ as $t\uparrow \infty$. In particular, we provide a constructive method for global Lyapunov functions for gradient-like random dynamical systems.
Access status: Open Access ,
Some constructions of Lyapunov function for linear extensions of dynamical systems
(2011) Kulik, Viktor; Tkocz-Piszczek, Ewa
In this note we consider some sets of linear extensions of dynamical systems and research regularity by means of the sign-changing Lyapunov function. We examine some constructions of Lyapunov functions for given systems.
Access status: Restricted ,
Stabilność liniowych hybrydowych układów równań różniczkowych zwyczajnych
(Data obrony: 2013-07-12) Knap, Aleksandra
Wydział Matematyki Stosowanej
Access status: Restricted ,
Wspólne rozwiązanie równania Lapunowa dla macierzy stowarzyszonej Frobeniusa i macierzy o wymiarach 2x2
(Data obrony: 2013-07-12) Skupień, Sabina
Wydział Matematyki Stosowanej