For discrete-time positive Lur'e systems, incremental l1 and l_infinity gains are upper-bounded by linear programs, and a linear program designs state feedback to regulate the l_infinity gain.
A linear dissipativity approach to incremental input-to-state stability for a class of positive lur’e systems,
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Incremental Gain Computation and Regulation of Discrete-time Positive Lur\'e Systems using Linear Programming
For discrete-time positive Lur'e systems, incremental l1 and l_infinity gains are upper-bounded by linear programs, and a linear program designs state feedback to regulate the l_infinity gain.