On the stability of planar randomly switched systems
On the stability of planar randomly switched systems
Consider the random process ${(X_{t})}_{t\geq0}$ solution of $\dot{X}_{t}=A_{I_{t}}X_{t}$, where ${(I_{t})}_{t\geq0}$ is a Markov process on $\{0,1\}$, and $A_{0}$ and $A_{1}$ are real Hurwitz matrices on $\mathbb{R}^{2}$. Assuming that there exists $\lambda\in(0,1)$ such that $(1-\lambda)A_{0}+\lambda A_{1}$ has a positive eigenvalue, we establish that $\|X_{t}\|$ may converge to 0 or $+\infty$ depending …