Optimal control of stochastic linear systems by discrete output feedback

The sequential minimization of quadratic cost functions is considered for stochastic linear systems. The class of admissible controls is constrained to be the set of linear functions of the output, sampled at discrete instants of time. Unlike other formulations, sequential minimization results in output-feedback controllers that can be computed on-line. The state of the optimum closed-loop system tends to zero in a finite time interval for almost all sample paths. These results are specialized to deterministic systems to show that any state
X_{N} \epsilon R^{n}
is reachable by discrete output feedback, provided the system under consideration is discrete-time completely observable and completely controllable.