Investigation of the ICD structure of systems defined by state-space models: International Journal of Control

The individual channel design (ICD) pole-zero structure of systems defined by linear state-space models is investigated. The existence of ‘fictitious’ cancelling poles and zeros and highly structured plant transfer-function matrices leads to a requirement, within ICD, that these systems be handled differently from systems given directly (Leithead and O'Reilly 1992 b) in transfer-function matrix form. Both the pole-zero structures of multiple-channels and of multiple-channels with infinite gain are presented, and it is noted that multiple-channel zeros which coincide with the plant poles are fictitious. A similar statement of pole-zero structure is made for each of the m open-loop Individual Channels Cj. Further, the number Z of RHPZs of Channel Cj is given by Z = N + P − Q where N is the net number of clockwise encirclements of the point (1,0) by the Nyquist plot of the multivariable structure function γj(s), P is the number of RHPPs of γj(s), and Q is the number of RHPPs of the plant. Finally, it is established that weak feedback around an individual plant transfer function element can be used to stabilize the plant, render specific individual plant transfer function elements minimum phase, and render specific plant sub-matrices minimum phase. © 1994 Taylor & Francis Ltd.