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Pole assignment for linear and quadratic systems with time-delay in control


Correspondence to: E. K-W. Chu, School of Mathematical Sciences, Building 28, Monash University, VIC 3800, Australia.



We consider the pole assignment problems for time-invariant linear and quadratic control systems, with time-delay in the control. Closed-loop eigenvectors in X = [x1, x2, ⋯  ] are chosen from their corresponding invariant subspaces, possibly optimizing some robustness measure, and explicit expressions for the feedback matrices are given in terms of X. Condition of the problems is also investigated. Our approach extends the well-known Kautsky, Nichols, and Van Dooren algorithm. Consequently, the results are similar to those for systems without time-delay, except for the presence of the ‘secondary’ eigenvalues and the condition of the problems. Simple illustrative numerical examples are given. Copyright © 2011 John Wiley & Sons, Ltd.