Approximate Discrete-Time Feedback Linearization of a Constant-Parameter Riccati System

An approximate, discrete-time, linearizing feedback law is presented for systems whose dynamics can be modeled by a Riccati differential equation with constant parameters. Although the original equation is affine, its exact (step-invariant) discrete-time model, which gives the exact value at the sampling instants for any sampling interval for piece-wise constant inputs, is not. Since this fact can make the control law synthesis intractable, approximations of the exact model into forms that are simpler for control input synthesis are proposed. In particular, the first- and second-order Pade approximations as well as the proposed approximations are considered. Simulation studies are carried out to show that the proposed method gives the best results among those considered in this study; i.e., the sampled-and-held method, those based on Pade approximations, and the proposed method