Stability Of Two Kinds Of Distributed Parameter Systems

Control mode, controlled object or controller need to be described by distributed parameter control system called distributed parameter control system. In engineering technology, the control device or the execution mechanism may also be distributed parameter system in addition to the controlled object. The stability of distributed parameter systems is one of the main research contents of distributed parameter control theory, which has been widely studied in recent years. In this context, the exponential stability of the mono-tubular heat exchanger equation with boundary observation possessing a time delay and inner control is investigated through a simply proportional feedback. Moreover, the quasi-compactness and irreducibility of queueing models is also investigated in this thesis.For the mono-tubular heat exchanger equation with time delay in boundary observation, the close-loop system is firstly translated into an abstract Cauchy problem in the suitable state space. A uniformly bounded 0C-semigroup generated by the close-loop system, which means that the unique solution of the system exist, is shown. Secondly, the spectrum configuration of the closed-loop system is analyzed and the eventual differentiability and the eventual compactness of the semigroup are shown by the resolvent estimates on some resolvent set. This implies that the spectrum determined growth assumption hold. Finally, a sufficient condition, which is on the physical parameters in the system and independent of the time delay, of the exponential stability of the closed-loop system is given.Since quasi-compactness and irreducibility of semi-group and the exponential stability of system has tight relation, the quasi-compactness and irreducibility of two queueing systems are investigated by abstract functional analytical methods. In this paper, the quasi-compactness and irreducibility of two queueing systems are investigated by abstract functional analytical methods. More precisely, the systems fit into Greiner’s framework and Greiner’s idea of boundary perturbation of the generator is utilized. Quasi-compactness or irreducibility of the semi-group generated by the system operator is obtained through special properties of the boundary perturbation operators. Moreover, the exponential stability of the queueing models is analyzed based on the quasi-compactness and irreducibility.