A step toward a unified treatment of continuous and discrete time control problems

Abstract

In this paper we introduce a new approach for a unified theory for continuous and discrete time (optimal) control problems based on the generalized Cayley transformation. We also relate the associated discrete and continuous generalized algebraic Riccati equations. We demonstrate the potential of this new approach by proving a new result for discrete algebraic Riccati equations. But we also discuss where this new approach as well as all other approaches still is nonsatisfactory. We explain a discrepancy observed between the discrete and continuous case and show that this discrepancy is partly due to the consideration of the wrong analogues. We also present an idea for an implication scheme that relates general theorems for discrete and continuous control problems.