Componentwise stabilizability and detectability of linear systems

The componentwise asymptotic stability (CWAS) and componentwise exponential asymptotic stability (CWEAS), introduced and characterized in previous works, are used to define componentwise stabilizability / detectability and componentwise exponential stabilizability / detectability for both discrete- and continuous-time linear systems. The approach brings a substantial refinement to the classical concepts of stabilizability / detectability, by ensuring an individual monitoring of each state variable. Necessary and sufficient conditions are formulated for the existence of componentwise exponential stabilizability / detectability with guaranteed performance. These conditions represent the theoretical background for the synthesis procedures of CWEAS regulators / observers, which are developed as constrained nonlinear optimization problems, so as to ensure the computational tractability.