Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces.Secondly,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of GE-semigroup,and the dual principle is given.Thirdly,an illustrative example is given.

Impulse Controllability and Impulse Observability of Stochastic Singular Systems

This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.

Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Observer-Based Controller Design for Singular Stochastic Markov Jump Systems with State Dependent Noise

This paper is concerned with the problem of observer-based controller design for singular stochastic Markov jump systems with state-dependent noise. Two concepts called "non-impulsiveness"and "mean square admissibility" are introduced, which are different from previous ones. Sufficient conditions for the open-and closed-loop singular stochastic Markov jump systems with state-dependent noise to be mean square admissible are provided in terms of strict LMIs. The controller gain and the observer gain which guarantee the resulting closed-loop error system to be mean square admissible are obtained in turn by solving the strict LMIs. A numerical example is presented to show the efficiency of the design approach.

State Estimation of Discrete Stochastic Singular System

In this paper, a state estimation problem in discrete\|time stochastic singular systems is investigated. It has been proved that the optimal state estimation problem of a discrete\|time stochastic singular system is equivalent to the optimal control problem of a deterministic singular system.