Stability regions of linear canonical systems with periodic coefficients (Q2714635)

In the paper the canonical system NEWLINE\[NEWLINE J\dot x = H(t)x,\quad J = \left\| \begin{matrix} 0 & -I_n\\ I_n & 0\end{matrix} \right\| ,\quad x\in \mathbb{R}^{2n}\tag{1} NEWLINE\]NEWLINE is considered, where \(\,H(t) = H(t+T)\,\) is a symmetric piecewise continuous matrix. The author proposes a new definition of the index of stability domain of the system (1) and presents a simple proof for the Helfide-Lidskij theorem on the structure of stability domains. The directed convexity of stability domains is discussed. The Hill equations are considered as examples.