1. Robust control and time-domain specifications for systems of delay differential equations via eigenvalue assignment
- Author
-
Yi, Sun, Nelson, Patrick W., and Ulsoy, A. Galip
- Subjects
Eigenvalues -- Research ,Time-domain analysis -- Research ,Invariants -- Research ,Differential equations -- Delay equations ,Differential equations -- Research ,Engineering and manufacturing industries ,Science and technology - Abstract
An approach to eigenvalue assignment for systems of linear time-invariant (LTI) delay differential equations (DDEs), based upon the solution in terms of the matrix Lambert W function, is applied to the problem of robust control design for perturbed LTI systems of DDEs, and to the problem of time-domain response specifications. Robust stability of the closed-loop system can be achieved through eigenvalue assignment combined with the real stability radius concept. For a LTI system of DDEs with a single delay, which has an infinite number of eigenvalues, the recently developed Lambert W function-based approach is used to assign a dominant subset of them, which has not been previously feasible. Also, an approach to time-domain specifications for the transient response of systems of DDEs is developed in a way similar to systems of ordinary differential equations using the Lambert W function-based approach. [DOI: 10.1115/1.4001339]
- Published
- 2010