Synthesis of standard variable structure systems with time delay

We consider variable structure systems (VSS) in presence of a time delay in phase variables. The parametric conditions of existence of sliding modes for linear switching function in VSS with standard control laws are adduced. Ample functional potentials of standard control laws are shown in contrast to nonstandard laws of control, which are connected with application of complex and sticky automata of switching functional on terminal elements. It is possible to overcome difficulties arising due to the effect of delay on analysis of the system stability by means of proper choice of the Lyapunov-Krasovski V-functional as "full quadratic form of variables plus integral from the delay term squared".