Robust semiglobal stabilization of the second order system by relay feedback with an uncertain variable time delay

Eugenii Shustin (1) , Leonid Fridman (2) , Emilia Fridman (3) , Fernando Castaños (4)

1 TAU - School of Mathematical Sciences [Tel Aviv]
2 UNAM - Department de Control, División de Ingeniería Eléctrica
3 Department of Electrical Engineering
4 L2S - Laboratoire des signaux et systèmes

We present sufficient conditions for robust relay-delayed semiglobal stabilization of second order systems, which relate the upper bound to an uncertain time delay and the parameters of the plant. We also suggest an algorithm of delayed relay control gain adaptation for semiglobal stabilization, which is based on delayed information about the sign of the controlled variable only. The proposed algorithm suppresses bounded uncertainties in the time delay; that is, being designed for the upper bound of uncertainty in the time delay, the control law ensures semiglobal stabilization independently of any variable time delay obeying the given upper bound.

Keywords: variable structure systems; time delay; robust control

Domains: Automatic

Eugenii Shustin, Leonid Fridman, Emilia Fridman, Fernando Castaños. Robust semiglobal stabilization of the second order system by relay feedback with an uncertain variable time delay. SIAM Journal on Control and Optimization, 2008, 47, pp.196 -- 217. ⟨hal-00218262⟩