L2-Stabilizability Conditions for a Class of Singularly Perturbed Delayed Systems

V.Y. Glizer (Israel)


Time delay system, singular perturbation, stabilizability.


A singularly perturbed linear time-invariant controlled sys tem with point-wise and distributed delays in the state vari ables is considered. The delays are of two kinds: nonsmall in the slow and small in the fast state variables. Two much simpler parameter-free subsystems (the slow and fast ones) are associated with this system. It is established in the pa per that L2 -stabilizability of the slow and fast subsystems yields L2 -stabilizability of the original system for all suffi ciently small values of the parameter of singular perturba tion. Illustrative examples are presented.

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