Abstract
The relay control systems with time delay are considered. We show that the time delay does not allow to realize an ideal sliding mode, but implies oscillations, whose stability is determined by one discrete parameter-oscillation frequency. Any motion of scalar discontinuous delay system turns into a steady mode-a motion with a constant frequency. Such steady modes have all properties of sliding modes. The problem of stability of steady modes in three main cases autonomous, quasiautonomous and periodic is considered. It is shown that in autonomous and quasiautonomous cases only steady modes with zero frequency are stable. At the same time this modes are non-asymptotically stable. The structural stability of steady modes in the periodic case is investigated. The resonances are singled out. The existence of the slow stable periodic solution of the multidimensional singularly perturbed relay system with time delay is proved. At last, we design a direct adaptive control of relay type with time delay that extinguishes parasite auto-oscillations in this model.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
