Almost non-interacting control by measurement feedback

• Published in: Systems & control letters Vol. 9; no. 1; pp. 7 - 16
• Main Author: van der Woude, J.W.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 1987; Elsevier
• Subjects: Almost non-interacting control; Applied sciences; Common solution to a pair of linear matrix equations; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Exact sciences and technology; Measurement feedback; Measurement feedback; Common solution to a pair of linear matrix equations; Almost non-interacting control; MIMO system; Closed loop; Transfer matrix; Almost non interactive control; Linear equation; Necessary and sufficient condition; Compensator; Matrix equation; Equation system
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/0167-6911(87)90003-X

Consider a linear system Σ that, apart from a control input and a measurement output, has two exogeneous inputs and two exogenous outputs. Controlling such a system by means of a measurement feedback compensator Σ c results in a closed loop system with two inputs and two outputs. Hence, the closed loop transfer matrix can be partitioned as a two by two block matrix. The problem addressed in this paper consists of the following. Given Σ and any positive number ge, is it possible to find Σ c such that the off-diagonal blocks of the closed transfer matrix, in a suitable norm, are smaller than ϵ? For the solvability of this problem necessary and sufficient conditons will be derived.