An application of the induced matrix norm in the minimum-energy design of perfect control algorithm

Abstract

In the previous research study it has been pointed out that employing the approximation of the induced matrix norm can be useful during design of minimum-energy perfect control law for LTI MIMO discrete-time state-space plants. It has also been shown that this scenario was related to the case involving the closed-loop control matrix norm being less than unity, which was preserved by proper selection of applied nonunique inverses. This paper focuses on the systems which have been excluded from our past considerations. The methodology of minimum-energy approach for plants with norm greater than one is postulated here and some peculiarities in this matter additionally are given. This innovative method allows to predefine in a simple way a minimum-energy behavior of this intriguing control procedure.