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# Questions tagged [stability]

Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)

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### On Designing Some Optimal Control Problems

In the context of a dynamical systems, some states may not be attainable with scalar controls from $L^1(0,T)$, but they may be reachable with feedback controls. If we know that the system is null ...
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### Some question about (semi-)stable sheaves

Let $X$ be a projective normal variety over $\mathbb C$, I have several questions about semi-stable sheaves: Question 1. Suppose that $E$ is a pure sheaf such that $HN_*(E)$ is the Harder-Narasimhan ...
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### Asymptotic behaviors of equilibrium points of a switching SDE with Levy jumps?

Consider the following paper titled: Stochastic regime switching SIR model driven by Lévy noise, authored by Yingjia Guo. Link: https://www.sciencedirect.com/science/article/pii/S0378437117302145 The ...
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### Boundedness of solutions to second order linear damped ODE

Let $f:\mathbb{R}^n\to\mathbb{R}$ be a polynomial with $\inf_{x\in\mathbb{R}^n}f(x)>-\infty$. If the solution to $x'(t)+\nabla f(x(t))=0$ is bounded for any initial point $x(0)=x_0\in\mathbb{R}^n$, ...
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### Conditions for a block matrix to be Hurwitz stable

Consider the following block matrix: $$A = \begin{bmatrix} 0 & I\\ -M & -I \end{bmatrix}$$ Suppose matrix $M$ is positive definite and satisfies $M\succeq \alpha I$, where $\alpha>0$ is a ...
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### $L^p$-continuity for discrete linear causal systems

Let $p \in [1, +\infty)$, $(b_0(n)), \dots (b_m(n)), (a_1(n)), \dots, (a_m(n))$ suitable sequences of real numbers and consider the map $\phi: \ell^p \to \ell^p$, $x \mapsto y$ defined by: \begin{...
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### Selecting a suitable Lyapunov function for the following systems?

i) SI MODEL Consider \begin{align} \frac{dS}{dt} &= \mu N -\frac{\beta S I}{N} - \nu S\\[2ex] \frac{dI}{dt} &= \frac{\beta S I}{N} -\nu I \end{align} Where $N=S+I$ is the total population. If ...
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