Output Feedback Control With Spectrum Constraints For Stochastic Systems Subject To Multiplicative Noises

During the past several decades,the stochastic system has received lots of research attention since it plays a prominent role in many application areas such as finance,economics and bioinformatics.In practical application,due to the existence of noise,the stability of the system usually becomes worse or even leads to unstable and further affects other performances.Therefore,this thesis aims to cope with stability of stochastic systems with multiplicative noises by using spectrum technique.In virtue of the matrix theory and stochastic analysis method,the H_?control problem and the mixedH₂/H_?control problem for stochastic system is settled thoroughly.The gain matrix of output feedback controller with spectrum constraints is solved in terms of linear matrix inequalities.The main work of this paper can be summarized into the following three parts:1.The problem of static output feedbackH₂/H_?control with spectrum constraints is studied for linear continuous-time stochastic systems with state dependent noises.More specifically,on the one hand,the notion of D(-?,-?)stability for continuous-time stochastic systems is defined by using the spectrum technique,and a sufficient condition is derived for the closed-loop system to be D(-?,-?)-stable.On the other hand,theH₂/H_?control problem is further investigated.By solving the optimization problem,the parameters of the static output feedback controller and the optimalH₂/H_?performance indexes are obtained.2.By means of the spectrum technique,the problem of H_?consensus control with spectrum constraints for continuous-time multi-agent systems with state-,control-,and disturbance-dependent noises.One of the critical problems is the design of the consensus controller which enable all agents to reach some expected characteristics by utilizing local neighboring information.In virtue of the stochastic analysis method and Kronecker product,a a sufficient condition is derived for the closed-loop system to be D(-?,-?)-consensus with H_?performance.3.The problem of static output feedback H_?control with spectrum constraints is investigated for a class of linear discrete-time stochastic systems with packet dropouts.The stochastic system under study involves state-,control-,and disturbance-dependent noises,and packet dropouts are supposed to obey the Bernoulli random binary distribution.The concept of D(0,?)stability is introduced for linear discrete-time stochastic systems based on the spectrum technique.A sufficient condition is derived for the closed-loop system to be D(0,?)-stable with H_?performance,and the parameters of the controller are obtained by means of matrix inequality technique.Furthermore,in the example simulation part,the relationship between the decay rate of system and packet dropouts,H_?performance index is analyzed.