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Abstract
This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delay-dependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is main-tained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer's choice of a (delay-dependent) arbitrary spectrum assignment objective.
Highlights
Time-delay systems have received an increasing interest in the last years
It is proved that the controller synthesis problem is solvable, in general, with a realizable delay-dependent controller for any prefixed spectrum if the plant transfer function P(s) and that obtained as a particular case when neglecting all the delayed dynamics, namely P0(s), are both cancellation free
This paper has dealt with the synthesis problem of pole-placement-based controllers for systems with point delays
Summary
Time-delay systems have received an increasing interest in the last years It is proved that the controller synthesis problem is solvable, in general, with a realizable delay-dependent controller for any prefixed (either finite or delay-dependent) spectrum if the (delay-dependent) plant transfer function P(s) and that obtained as a particular case when neglecting all the delayed dynamics, namely P0(s), are both cancellation free. The first one consists of the solution of a finite set of nested Diophantine equations of polynomials, all of which being sequentially solvable if and only if P0(s) has no zero-pole cancellation This part of the design sets a part of the controller numerator and denominator quasipolynomials while generating an extra unsuitable dynamics in the closed-loop spectrum that is inherent in the proposed synthesis method.
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