On the existence of proportional-integral observer for the state estimation of linear time-invariant systems

Abstract In this paper, the explicit necessary and sufficient conditions are established for the existence of proportional-integral observer for the state estimation of linear time-invariant continuous-time systems. In particular, it is proven that for a given linear time-invariant continuous-time system of order n , having m inputs and p linearly independent outputs, a proportional-integral observer of order n can be constructed if and only if the given system is detectable. Furthermore a simple procedure is given for the construction of proportional-integral observer. Our approach is based on properties of real and polynomial matrices.