A New Design Procedure of the Pole-Placement and the State Observer for Linear Time-Varying Discrete Systems

Abstract

This paper presents a new design procedure of the pole placement and the Luenberger observer for linear time-varying discrete systems. First, a simple calculation method to derive the pole placement state feedback gain for linear time-varying discrete systems is proposed. 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 new 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. In general, the equivalent transformation of the time-varying linear system does not preserve the stability. The paper also shows the condition of the stability of the closed loop system. Then, this method is applied to the design of the observer. For this purpose, the anti-causal system is introduced. Using the dual property of this system, the observer gain vector is calculated by the proposed simple design technique of the pole placement control.