OPTIMAL TRACKING FOR BILINEAR STOCHASTIC SYSTEM DRIVEN BY FRACTIONAL BROWNIAN MOTIONS

This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.

Some new results on time-varying Stratonovich and Itô bilinear stochastic systems

The bilinear stochasticity of dynamical systems is attributed to the input–output coupling term,where the input is a random input and the state is the output of dynamical systems.Stochastically influenced bilinear systems are described via bilinear stochastic differential equations.In this paper,first we construct a mathematical method for the closed-form solution to a scalar Stratonovich time-varying bilinear stochastic differential equation driven by a vector random input as well as the Itôcounterpart.Second,the analytic results of the paper are applied to an electrical circuit that assumes the structure of a bilinear stochastic dynamic circuit.The noise analysis of the bilinear dynamic circuit is achieved by deriving the mean and variance equations as well.The theory of this paper hinges on the‘Stratonovich calculus’,conversion of the Stratonovich integral into the Itôintegral and characteristic function of the vector Brownian motion.The results of this paper will be useful for research communities looking for estimation and control of bilinear stochastic differential systems.

Observer-Based Fuzzy Control Design for Discrete-Time T-S Fuzzy Bilinear Stochastic,Systems with Infinite-Distributed Delays

This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays. Based on the piecewise quadratic Lyapunov functional （PQLF）, the fuzzy observer-basedcontrollers are designed for T-S fuzzy bilinear stochastic systems. It is shown that the stability in the mean square for discrete T-S fuzzy bilinear stochastic systems can be established if there exists a set of PQLF can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities （LMIs） constraints. An iterative algorithm making use of sequential linear programming matrix method （SLPMM） to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.

T-S Fuzzy Stochastic Bilinear Model and Fuzzy Controller Design Based on Switching Piecewise Lyapunov Functions

Based on a piecewise quadratic lyapunov function （PQLF）, this paper presents stochastic stability analysis and synthesis methods for ItO and discrete T-S fuzzy bilinear stochastic systems. Two improved stochastic stability conditions have been established in terms of linear matrix inequalities （LMIs）. It is shown that the stability in the mean square for T-S fuzzy bilinear stochastic systems can be established if a PQLF can be constructed. Considering the established stability criterion, the controller can be designed by solving a set of （LMIs）, and the closed loop system is asymptotically stable in the mean square. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.