Output Regulation of Linear Stochastic Systems

We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve ideal full-information output-feedback problems, obtaining perfect, but non-causal, asymptotic regulation. A characterisation solvability is deduced. point out that problems cannot be solved in practice because they unrealistically require Brownian motion affecting system available feedback. Drawing from solution, approximate versions which do not yield perfect tracking can realistic scenario. These solutions rely on two key ideas: first introduce discrete-time a-posteriori estimator variations obtained causally by sampling state or output; second hybrid observer regulator scheme employ estimated variations. The solution tends to as period zero. proposed theory validated circuit subject electromagnetic noise.