Admissibility and Observability of Jeffreys Type of Overdamped Second Order Linear Systems

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 466-486, February 2024.
Abstract. We study Jeffreys-type overdamped second order linear systems with observed outputs in the setting of Hilbert spaces. The state equation comes from an overdamped second order linear partial differential equation which is wave-like but was proposed to describe heat conduction. It results from adopting the Jeffreys law of constitutive relation for heat flux, rather than the usual Fourier law. Sufficient conditions for infinite-time admissibility of the system observation operator and system observability are obtained. In the general case, we obtain the infinite-time admissibility from that of the first order Cauchy system, which is done by employing the Hardy space approach. In the special case when the operator in the state equation is negative definite, we derive the infinite-time admissibility and system observability using a semigroup approach. Illustrative examples are given.