The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.
"On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems." Abstr. Appl. Anal. 2013 (SI41) 1 - 12, 2013. https://doi.org/10.1155/2013/639576