Structural controllability and observability in closed loop for LTI stable systems

Linear Time Invariant (LTI) Multi-Input Multi-Output (MIMO) stable systems modeled in bond graph and described by their junction structures, are considered. Junction structures for the sensitivity and complementary sensitivity functions, are proposed. These structures are function of the free parameter of the family of stabilizing compensators, and allow to get necessary and su??cient conditions for structural controllability and observability in closed loop. Also, these structural properties are design criterions for the free parameter of the stabilizing compensator, which is implemented on the Internal Model Control (IMC) feedback configuration. Also, the free parameter is gotten from its state space realization, for Single-Input Single-Output (SISO) systems. Moreover, a junction structure for the stabilizing compensator, function of the free parameter, is presented. Based on this structure, a necessary condition for the structural stability of the compensator, is given. The results are illustrated on a damping mechanical system.