Abstract
In this paper we present a method for the simulation of continuous-time bilinear systems ẋ ( t ) = Ax ( t ) + Nx ( t ) u (t) + bu ( t ), that can be used to realize bilinear observers for real-time control systems. Our method attempts to approximate the state variable x ( t ) in the bilinear term x ( t ) ut ) with an interpolation polynomial and treats this term as an independent input signal, then solves the bilinear state space equation like a linear system equation. The method yields, especially for large integrating step sizes, a more exact solution than a 4th order Runge-Kutta method. Even if the Runge-Kutta method becomes unstable the method works well.
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