A new criterion for strong observability

Apart from controllability and observability an important concept in linear system theory is strong observability [1] — [4j. This latter concept appears naturally in the study of singular quadratic optimal control problems [4]. A strongly (alternatively perfectly) observable is that system for which an observer can determine the state vector x(0) = x0 with the knowledge of output y(t) only, information regarding input u(t) not required. The criteria of these concepts in terms of system matrices (A, B, C, D) are well known [ l ] . In this correspondence we shall formulate these criteria in terms of parameters contained in transfer-function matrix representation of the system in the form P(s) <z(s). Given a transfer-function matrix description T(s) of a system it may be of interest to decide whether any minimal realization of this system is strongly observable or not. So one has to find out at first the minimal realization by applying the existing methods and then to apply the available criteria given in terms of state space descrip^tion to check whether this realization of the system is strongly observable or not. If instead one could check the strong observability of state realization with the help of parameters of T(s) the first step could be avoided to get the desired information. The aim of this short note is to formulate a criterion of strong observability of the state-space realization of a given system in terms of the parameters of its transferfunction matrix. The linear time-invariant systems under our investigation are represented by the p x m transfer-function matrix