Control And Design For Stochastic Bilinear Systems

As a special kind of nonlinear systems, bilinear system models are simpler than nonlinearsystems in many practical engineering applications, and compared with linear systems they aremore accurate to describe the dynamic systems. So the study of bilinear systems has been re-ceived considerable attention in the last half century. Considering the large amounts of uncertainphenomena existing in actual dynamic systems, this thesis investigates the problem of controland filtering designs for stochastic bilinear system by using Lyapunov functional method andlinear matrix inequality(LMI) technique.The main contents are given as follows:First, for a class of stochastic bilinear delay systems, a sufficient mean square asymp-totically stability condition is established by introducing a nonlinear controller. Based on thecondition, a nonlinear state feedback controller design method is proposed. Moreover, for thesystems with immeasurable states, a Luenberger observer is also designed for the systems underconsideration. The designed observe enables the error system to be asymptotically stable in themean-square sense.Second, based on storage energy function method, passivity condition for a class of s-tochastic bilinear delay systems with multiple dimensional bounded control is presented, byintroducing a bounded nonlinear feedback controller. Moreover, input and output strict stochas-tic passivity, the relationship between output strict stochastic passivity and stochastic L2gainfrom input to output, and stochastic KYP (Kalman-Yakubovich-Popov) property for stochasticbilinear delay systems have been considered.Third, this thesis deals with the design of a reduced-order H2/H∞filter for a stochasticbilinear system. The problem is transformed into the search of a unique gain matrix by usingSylvester-like constraints. A design method of H∞filter with a prescribed H∞performanceindex is presented, and the worst case disturbance attenuation of H∞filtering is presented.Finally, the mixed H2/H∞filtering design problem is transformed into a constrained optimiza-tion problem in terms of LMI constraints.