Time-averaged robust control of stochastic partially observed uncertain systems

We consider a linear-quadratic infinite-horizon time-averaged guaranteed cost control problem for stochastic uncertain systems with output measurement. A new class of uncertainty is introduced that satisfies a stochastic relative entropy constraint. The solution of a specially parametrized risk-sensitive stochastic control problem based on a pair of algebraic matrix Riccati equations is used to establish a guaranteed cost control law for the original uncertain system. It is shown that this guaranteed cost control absolutely stabilizes the system