Distributed delay systems with truncated Gamma distribution: instability regions∗

The paper presents necessary stability conditions for distributed delay systems with truncated Gamma distribution. Motivated by the known Lyapunov equation for delay free linear systems, these conditions depend only on the Lyapunov delay matrix of the system. In conjunction with the Dsubdivision boundaries, the necessary conditions are employed to find instability regions in the space of parameters of the system. The result is illustrated by an example.