Analyticity conditions of characteristic and disturbing quasipolynomials of hybrid dynamical systems

Hybrid dynamical systems (HDS) are connected by means of the boundary conditions and the constraint's conditions systems of ordinary differential equations and partial differential equations with the corresponding initial conditions. Check the stability of HDS can be performed on the basis of the "fast" algorithm for the application which requires analytic characteristic and disturbing quasipolynomials of HDS in the right half-plane and near the imaginary axis. In this paper we formulate and prove the analyticity conditions of the characteristic and disturbing HDS quasipolynomials. Mathematical models of control objects with distributed parameters in space, matching the thermal conductivity and diffusion processes, the dynamics of support layers of viscous incompressible fluid, as well as the dynamics of the elastically deformable medium taking into account the internal friction.