The Hankel-type L q /L p Induced Norms of Positive Systems Across Switching

International audienceThe Hankel-type L q /L p induced norms across a single switching over two linear timeinvariant (LTI) positive systems are discussed. The norms are defined as the induced norms from vector-valued L p-past inputs to vector valued L q-future outputs across a switching at the time instant zero. The Hankel-type L 2 /L 2 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 L q /L p 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 (LP) and semidefinite program (SDP). The SDP-based characterizations are useful for the analysis of the Hankel-type L q /L p induced norms where the systems of interest are affected by parametric uncertainties