The Stability And Observability Of Poisson Jumps Systems

In recent years, more and more scholars pay close attention to stochastic systems with Poisson jumps because these systems can better describe the sudden stochastic disturbance. Stochastic systems with Poisson jumps play a main role in physics, chemistry, engineering,finance, biological systems, and other fields, It has important significance for research stochastic systems with Poisson jumps.This paper mainly studies the stability and exact observability of linear stochastic systems driven by Poisson jumps and Brownian motion.The main results are as follows:On the basis of linear operator, a necessary and sufficient condition for the stability of linear stochastic systems is obtained. Generalize the concept "unremovable spectrum" and the criterion for unremovable spectrum is given. A theorem use "unremovable spectrum" as the tool, to judge the system can stabilizability or not, is presented. On the basis of defines interval stability of linear stochastic systems with spectrum of operator, this paper studies some relationships among the interval stability and the convergence rate of system state. The criterion for interval stability of stochastic systems is obtained with linear matrix inequality and Schur lemma. At last, this paper defines exact observability and exact detectability and has analysis some relationships among stability, exact observability, exact detectability and generalized Lyapunov inequality. Numerical examples in some chapters are given in order to facilitate understanding.