A new discrete-time linearization feedback law for scalar Riccati systems

A new discrete-time feedback linearization law is proposed for a scalar Riccati system with constant parameters. The method uses a discretization method proposed recently by the same authors, where the so-called discrete-time integration gain is discretized such that the resulting model is approximate for nonlinear systems but exact for linear cases. This discretization method is based on both continualization and discretization concepts, and is applicable to any system as long as its Jacobian matrix exists. It is shown that the proposed control law preserves the asymptotic stability of the desired linear system at sampling instants, while the popular forward difference and accurate Mickens methods in general do not. Simulation results demonstrate that the proposed method has better accuracy and tends to retain the desired dynamics for larger sampling intervals, than the other two methods.