Abstract
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.
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