Functional Controllability, Functional Stabilizability, and the Generalized Separation Principle

This paper introduces the new concepts of Functional Controllability and Functional Stabilizability, and establishes their duality with Functional Observability and Functional Detectability, respectively. A Generalized Separation Principle is presented, under which the classical Separation Principle emerges as a special case. Conditions for the existence of functional controllers of a specified order are derived. Notably, the proposed design framework does not require full controllability. In addition, a functional observer-based controller design is developed for systems that may be both uncontrollable and unobservable. The results presented extend and generalize the classical full-state observer based feedback control paradigm.