Abstract
In this paper, the concept of degrees of fixed modes is introduced for linear time-invariant control systems with constrained control structures, typically including decentralized control systems. It is defined by the minimal dimension of all eigenspaces of feedback system matrices for the fixed mode. It coincides with minimal multiplicity of the fixed mode as the transmission zero for nonsingular subsystems. Moreover, the existence of minimal effective subsystems corresponding to each fixed mode is guaranteed. The minimal number of additional interconnection gains (feedback links) necessary for eliminating the fixed mode are made clear based on the minimal effective subsystems. A dual characterization of the degree of fixed mode, the mnimal rank deficiency of feedback control structure matrices where the fixed mode is not the transmission zero of the corresponding subsystems, is also obtained. A method for eliminating plural fixed modes is proposed.
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