Existence of solutions to MIMO relay feedback systems

Abstract

This note studies the existence of solutions to MIMO linear systems under decentralized relay feedback containing hysterisis. A necessary and sufficient condition is presented to guarantee the extended solutions at the so-called intersecting instant. The suggested method is to examine the sign of the first non-zero derivative of each output right after the switches occur. Illustrative examples are given to show the cases of non-existence and non-uniqueness of solutions.