Given past, observations of a process, { y j , j < i}, suppose we arc interested in constructing one-step-ahead predictors of y i , denoted by $ i l i l . We show that, irrespective of whether the process { y j } is stationary or non-stationary, or whether it is scalaror vector-valued, the H2-optimal one-step-ahead predictor is also H"optimal. Since the H2 and H" paradigms represent fundamental...

In this article we provide a solution to the mixed H 2 =H 1 problem with reduced order controllers for time-varying systems in terms of the solvability of diierential linear matrix inequalities and rank conditions, including a detailed discussion of how to construct a controller. Immediate specializations lead to a solution of the full order problem and the mixed H 2 =H 1 problem for linear sys...