The Hankel-type Lq/LP induced norms of positive systems across switching

Y. Ebihara, D. Peaucelle, D. Arzelier

Research output: Contribution to journalConference articlepeer-review


The Hankel-type Lq/Lp induced norms across a single switching over two linear time-invariant (LTI) positive systems are discussed. The norms are defined as the induced norms from vector-valued Lp-past inputs to vector valued Lq-future outputs across a switching at the time instant zero. The Hankel-type L2/L2 induced norm across a single switching for general LTI systems is studied in details to evaluate the performance deterioration caused by switching. Thanks to the strong positivity property, we successfully characterize the Hankel-type Lq/Lp induced norms for the positive system switching even for p, q being 1, 2, ∞. In particular, we will show that some of them are given in the form of linear program and semidefinite program (SDP). The SDP-based characterizations are useful for the analysis of the Hankel-type Lq/Lp induced norms where the systems of interest are affected by parametric uncertainties.

Original languageEnglish
Pages (from-to)4719-4724
Number of pages6
Issue number2
Publication statusPublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: Jul 12 2020Jul 17 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


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