A control-theoretic study on iterative solutions to nonlinear equations for applications in embedded systems

In this paper, the fixed point iteration and Newton’s methods for iteratively solving nonlinear equations are studied in the control theoretical framework. This work is motivated by the ever increasing demands for integrating iterative solutions of nonlinear functions into embedded control systems. The use of the well-established control theoretical methods for our application purpose is inspired by the recent control-theoretical study on numerical analysis. Our study consists of two parts. In the first part, the existing fixed point iteration and Newton’s methods are analysed using the stability theory for the sector-bounded Lure’s systems. The second part is devoted to the modified iteration methods and the integration of sensor signals into the iterative computations. The major results achieved in our study are, besides some academic examples, applied to the iterative computation of the air path model embedded in the engine control systems.