This paper is concerned with the on-line health monitoring and damage assessment for structural and mechanical systems which are often used to model the dynamics of flexible space structures and civil infrastructure systems. It is assumed that damages result in the reduction of structural stiffness and it is desired to identify these damages on-line. An adaptive detection-diagnostic observer is proposed in order to detect the occurrence of failures and diagnose their nature and magnitude. Fault isolation estimators are then activated in order to provide information on the failure status and allow the controller to switch to a new signal that is appropriate for the system with a given failure mode. Both the full state and partial state cases are considered for the design of first a fault tolerant controller and then of a fault accommodating controller using LMI’s.