arXiv subjects

S. J. A. M. van den Eijnden

Publications and source records attributed to S. J. A. M. van den Eijnden.

2 recordsLinked to original sources

arXiv2026

Analysis and Design of Reset Control Systems via Base Linear Scaled Graphs

In this letter, we prove that under mild conditions, the scaled graph of a reset control system is bounded by the scaled graph of its underlying base linear system, i.e., the system without resets. Building on this new insight, we establish that the negative feedback interconnection of a linear time-invariant plant and a reset controller is stable, if the scaled graphs of the underlying base linear components are strictly separated. This result simplifies reset system analysis, as stability conditions reduce to verifying properties of linear time-invariant systems. We exploit this result to develop a systematic approach for reset control system design. Our framework also accommodates reset systems with time-regularization, which were not addressed in the context of scaled graphs before.

eess.SY↗

arXiv2024

The Non-Strict Projection Lemma

The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications we naturally encounter non-strict inequalities. As such, we present, in this note, a non-strict projection lemma that generalizes both its original strict formulation as well as an earlier non-strict version. We demonstrate several applications of our result in robust linear-matrix-inequality-based marginal stability analysis and stabilization, a matrix S-lemma, which is useful in (direct) data-driven control applications, and matrix dilation.

math.OC↗