Description:
In this paper introduce new approach forunified theory for continuous and discrete time(optimal) control problems based on thegeneralized Cayley transformation. We also relatethe associated discrete and continuous generalizedalgebraic Riccati equations. We demonstrate thepotential of this new approach proving newresult for discrete algebraic Riccati equations.But we also discuss where this new approach aswell as all other approaches still isnon-satisfactory. We explain a discrepancyobserved between the discrete and continuouscse and show that this discrepancy is partly dueto the consideration of the wrong analogues. Wealso present an idea for a metatheorem thatrelates general theorems for discrete andcontinuous control problems.