Title :
A Partial Solution of the Aizerman Problem for Second-Order Systems With Delays
Author :
Altshuller, Dmitry A.
Author_Institution :
Crane Aerosp. & Electron., Burbank, CA
Abstract :
This paper considers the Aizerman problem for second-order systems with delays. It is proved that for retarded systems with a single delay the Aizerman conjecture is true. For systems with multiple delays, a delay-dependent class of systems is found, for which the Aizerman conjecture is true. The proof is based on the Popov´s frequency-domain criterion for absolute stability.
Keywords :
Popov criterion; absolute stability; delays; frequency-domain analysis; Aizerman conjecture; Popov frequency-domain criterion; absolute stability; delay-dependent class; multiple delay; retarded system; second-order system; single delay; Aerospace electronics; Asymptotic stability; Cranes; Delay systems; H infinity control; History; Nonlinear equations; Stability criteria; Sufficient conditions; Transfer functions; Absolute stability; Aizerman problem; delay systems; frequency-domain methods;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.930193
