Comparison of different polynomial factorization approaches as an alternative to FIR approximation to solve the ℓ1 design problem

The aim of this paper is to present an application of polynomial factorization as an alternative to FIR approximation in the design of a ℓ₁ controller. The polynomial matrix fractions have been calculated for the H, U and/or V matrix transfer functions coming from the Youla parametrization of the plant to be controlled. Different approaches are possible depending on which one of the H, U and/or V matrix transfer functions are factorized. The objective of these approaches is to reduce the number of constraints, variables and/or non-zero coefficients in the Linear Programming problem to be solved for the ℓ₁ control design, and if possible, to accelerate the convergence of the upper and lower bounds of the ℓ₁ norm.