On the Pole-Placement and the Observer for Linear Time-Varying Systems

Abstract

A simple design method of the Luenberger observer for linear time-varying systems is proposed in this paper. The paper first propose the simple calculation method to derive the pole placement feedback gain vector for linear time-varying systems. For this purpose, it is shown that the pole placement controller can be derived simply by finding some particular "output signal" such that the relative degree from the input to this output is equal to the order of the system. Using this fact, the feedback gain vector can be calculated directly from plant parameters without transforming the system into any standard form. Then, this method is applied to the design of the observer, i.e., because of the duality of linear time-varying system, the state observer can be derived by un-stabilization of the state error equation.