Positivity And Stability Analysis For Stochastic Systems

Positive systems are a particular class of systems,which exist ubiquitously in real world including both the macroscopic fields and the micro domains.On the other hand,because of its stochastic uncertainty,stochastic system becomes one of the main research focuses for many researchers and the relating research results have not only great theoretical values but also extensive application benefits.For positive systems,their state vectors are required to be always positive,while for stochastic systems,the positivity investigation is still insufficient.In this thesis,based on the theory of linear programming,positivity and stability analysis are addressed for stochastic systems,and the main results are summarized as follows.(1)As for the stochastic systems in continuous-time form,firstly,certain constraints are tackled for the system matrices under which the considered systems are positive when there are no disturbance terms in the systems investigated.Secondly,based on the normal distribution of the disturbance term,sufficient conditions are derived in terms of the system matrices,under which the stochastic systems are positive in the sense of large probability.Next,stability issues are carried out for the considered systems,and sufficient criteria are derived.Finally,effectiveness of the obtained results is illustrated by several numerical examples.(2)When referring to the stochastic systems in discrete-time form,firstly,requirements on the system matrices are investigated for the general discrete systems to be positive.Based on this,definition is given for the stochastic system to be stochastically positive in the sense of probability,and the effect of the stochastic terms on the positivity of the considered systems is also discussed under different cases.Subsequently,stability is analyzed for such kind of systems.Finally,feasibility of the acquired criteria is demonstrated by illustrative numerical examples.