Optimal state regulation for uncertain state-space models

This paper studies the problem of state regulation for uncertain state-space models. It formulates a new weighted game-type cost function with bounds on the sizes of the uncertainties in the data. The cost function is of independent interest in its own right and its optimal solution is shown to satisfy an orthogonality condition similar to least-squares designs. When used in the context of state-space models, the solution leads to a control law with design equations that are similar in nature to LQR designs. The gain matrix, however, as well as the Riccati variable, turn out to be state-dependent in a certain way.