The lq/lp Hankel norms of discrete-time positive systems across switching

• Published in: SICE journal of control, measurement, and system integration Vol. 15; no. 2; pp. 109 - 118
• Main Author: Ebihara, Y.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 16.06.2022; Taylor & Francis Group
• Subjects: Hankel norms; l_q/l_p $ hankel norms; linear programming; nonnegative signals; positive system switching; semidefinite programming
• ISSN: 1882-4889; 1884-9970
• DOI: 10.1080/18824889.2022.2090801

In this study, we focus on the Hankel norms of linear time-invariant (LTI) discrete-time positive systems across a single switching. The Hankel norms are defined as the induced norms from vector-valued past inputs to vector-valued future outputs across a system switching and a state transition at the time instant zero. A closed-form characterization of the Hankel norm in this switching setting for general LTI systems can readily be derived as the natural extension of the standard Hankel norm. Thanks to the strong positivity property, we show that we can successfully characterize the Hankel norms for the positive system switching case even in some combinations of p, q being . In particular, some of them are given in the form of linear programming (LP) and semidefinite programming (SDP). These LP- and SDP-based characterizations are particularly useful for the analysis of the Hankel norms where the systems of interest are affected by parametric uncertainties.