Input-to-State Stability Analysis for Descriptor Homogeneous Systems

The paper is devoted to the problem of Input-to-State Stability (ISS) analysis for descriptor (singular) homogeneous systems. In particular, sufficient conditions for descriptor homogeneous systems to be ISS are proposed. It is shown that to verify the ISS property it is enough to establish asymptotic stability of a homogeneous descriptor system in disturbance-free case and check provided algebraic conditions. Based on this result it was shown that existing homogeneity-based finite-time controls and observers for linear descriptor systems provide the ISS property with respect to additive disturbances and measurement noise. The results are supported with numerical simulations of the generator system.