Sampled-Data Output Feedback Control of Linear Stochastic Systems with Noisy Sampling Intervals

The sampled-data output feedback control problem for a class of linear stochastic systems with noisy sampling intervals is studied. First, by using the relative properties of Wiener process, the conditional expectation and the law of total expectation, the dual randomness caused by the stochastic system and noisy sampling intervals is decoupled. The linear stochastic system is converted into an equivalent discrete-time system via the lifting technique. By the properties of matrix exponential function, together with the Kronecker product and the confluent Vandermonde matrix, the mathematical expectation of a product of multiple matrices is computed. The sampled-data output feedback controller is designed to stabilize the closed-loop system. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach.