Optimal H2 filtering for periodic linear stochastic systems with multiplicative white noise perturbations and sampled measurements

This paper addresses the problem of optimal H2 filtering for a class of continuous-time periodic stochastic systems with periodic sampled measurements. The class of admissible filters consist of deterministic continuous-time periodic systems with finite jumps. The optimal solution of the considered optimization problem is obtained by integrating a suitable generalized continuous-time Riccati equation with finite jumps. To illustrate the proposed filtering strategy, we consider a problem of field monitoring where sensors are distributed on a rectangular region in order to estimate the state of a diffusion process. We consider that the sensors and the filter communicate over a communication channel and we assume that the communication channel induces some communication constraints. More specifically, we consider a medium access constraint under which the shared network can only accommodate a limited number of simultaneous communications between components.