Exact Time-Discretization of Differential Riccati Equations with Variable Coefficients

Hiroaki Shiobara and Noriyuki Hori

Keywords

Exact discretization, Timevarying systems, Nonlinear systems, Differential Riccati equation with variable coefficients

Abstract

A method of exact discretization, which has been developed for linear time-varying systems, is extended to classes of time-varying nonlinear systems. It covers nonlinear systems whose dynamics are governed by a differential Riccati equation with variable coefficients. While numerical methods to such equations can involve errors using, for instance, Runge-Kutta schemes, the proposed discrete-time model generates a response that matches exactly that of the continuous-time original at sampling instants for any sampling period. This is achieved by a combination of exact linearization of a nonlinear system and subsequent exact time-discretization of the resulting linear system.

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