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We usually consider $\dot{x} = f(x)$, where $x$ is a vector. Now, I want to consider $$\dot{X}=f(X,U),$$ where $X$ is a square matrix $\mathbb{R}^{n\times n}$ state, $U$ is a square matrix variable $\...

Let $A\in\mathbb{R}^{n\times n}$ and consider the following dynamical system: $$ \frac{\mathrm{d}x(t)}{\mathrm{d}t} = -x(t)+\max\{0,Ax(t)\}, \ \ \ \ x(0)\in\mathbb{R}^n, $$ where $\max\{\cdot\}$ acts ...