On the Kalman-Yakubovich-Popov lemma for discrete-time positive linear systems: A novel simple proof and some related results

摘要

Theorems of alternatives on the feasibility of linear matrix inequalities (LMIs) are used in order to provide novel simple proofs for two considered versions of the Kalman-Yakubovich-Popov (KYP) lemma for discrete-time positive linear systems. Two different and novel recursive methods, to determine whether a positive matrix is or is not Schur, are obtained as an application of an existing connection between the strict inequality version of the KYP lemma for single-input single-output (SISO) discrete-time positive linear systems and a Schur matrix condition. Examples are included which provide illustration on these recursive methods.