A Kalman decomposition to detect temporal linear system structure

Abstract¿Feedback controllers for non-linear systems are often based on a linearized dynamic model. Such a linearized model may be temporarily uncontrollable and/or unreconstructable. This paper introduces the so-called differential Kalman decomposition of time-varying linear systems. It is based on differential controllability and differential reconstructability in conjunction with a linear time-varying continuous-time system description that allows the system structure and dimensions to change at certain timeinstants. We show how these together enable the detection of what will be called temporal system structure. This structure among other things reveals the temporal loss of controllability and/or reconstructability. Moreover this paper shows how time-varying state-dimensions enable a satisfactory realization theory for time-varying linear systems and how our Kalman decomposition is linked to the conventional ones.