A STEP TOWARD A UNIFIED TREATMENT OF CONTINUOUS AND DISCRETE-TIME CONTROL-PROBLEMS

In this paper we introduce a new approach for a unified theory for con tinuous and discrete time (optimal) control problems based on the gene ralized 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 discre te algebraic Riccati equations. But we also discuss where this new app roach as well as all other approaches still is nonsatisfactory. We exp lain a discrepancy observed between the discrete and continuous case a nd show that this discrepancy is partly due to the consideration of th e wrong analogues. We also present an idea for an implication scheme t hat relates general theorems for discrete and continuous control probl ems.