Rational approximation in linear systems and control

Rational Approximation Preconditioners for General Sparse Linear Systems

This paper presents a class of preconditioning techniques which exploit rational function approximations to the original matrix. The matrix is rst shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner to the original matrix. Since the incomplete factorization is made on a shifted matrix, a good...

On the Approximation of Pseudo Linear Systems by Linear Time Varying Systems (RESEARCH NOTE)

This paper presents a modified method for approximating nonlinear systems by a sequence of linear time varying systems. The convergence proof is outlined and the potential of this methodology is discussed. Simulation results are used to show the effectiveness of the proposed method.

Rational Approximation of Nonlinear Optimal Control Problems

In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compa...

Rational Systems in Control and System Theory

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...