ℓ∞-gain controller order reduction for discrete-time systems

Oussama Ajala, Simone Schuler, Frank Allgöwer

Abstract: This paper addresses the problem of controller order reduction for linear discrete-time systems. The proposed approach considers the minimization of an upper bound on the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -gain of the error between the system with the full controller and the system with the reduced controller. This upper bound is defined using the so-called star norm performance. The method considers explicitly time-domain performance as a reduction criterion, and thus making this approach suitable for the order reduction of the generally large order ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -optimal controllers. A sufficient solvability condition is provided in terms of LMIs with an extra equality constraint, which generally leads to a non-convex feasibility problem. An iterative algorithm with local convergence is used to overcome this problem. A numerical example is provided to confirm the effectiveness of the proposed controller reduction scheme.