Filtering on discrete-time stochastic systems with randomly occurring sensor delays via probability-dependent method

This paper deals with a filtering problem for discrete-time stochastic systems with sensor delays. The delayed measurements are subjected to a random way characterized by a random variable sequence following the Bernoulli distribution with time-varying probability. So as to solve the stability problem, we have constructed a Lyapunov functional. Then, a stability condition of the augmented system is derived, such that the admissible randomly occurring sensor delays, nonlinear disturbances and external noises, the augmented dynamics is exponentially mean-square stable. It is shown that the desired filter parameters can be derived in terms of the measurable probability by solving a convex optimization problem. Comparing with the conventional filters only with unchangeable structure, the gain-scheduled filter can be dynamically adjusted and has less conservatism, which is depending on the time-varying probability. The proposed design technique is finally verified in the light of a simulation example.