On optimal signal reconstruction over switching networks

In this paper we consider signal reconstruction over networks where the communication channel can be modeled as an input switching system (e.g., wireless communication). In particular, we formulate the design problem as a prototypical model matching problem where the various mappings involved belong to a class of input switching systems. The design interest is placed on minimizing the worst case performance of this model matching system over all possible switchings with either l₁induced norm or H₂ norm as the performance criterion. This minimization is performed over all stable receivers Q in the class of input switching systems. For the particular set-up at hand and in the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in terms of linear programs and quadratic programs respectively for the l₁-induced and H₂ norm optimizations. An approximate solution with any given precision is possible by finite truncation. Also, it is shown that the optimal receiver Q need not depend on the switching sequence in the cases of partially matched switching and unmatched switching, and that it can be obtained as a linear time-invariant (LTI) solution to an associated l₁ induced or H₂ norm optimization.