Switching control and time-delay identification

• Proposed a method of stabilizing dynamic systems with unknown time delay.
• Proposed a method for identifying the unknown time delay after the system is stabilized.
• Studied the supervisory control and time delay identification of linear time invariant and periodic systems.

The unknown time delay makes the control design a difficult task. When the lower and upper bounds of an unknown time delay of dynamical systems are specified, one can design a supervisory control that switches among a set of controls designed for the sampled time delays in the given range so that the closed-loop system is stable and the control performance is maintained at a desirable level. In this paper, we propose to design a supervisory control to stabilize the system first. After the supervisory control converges, we start an algorithm to identify the unknown time delay, either on-line or off-line, with the known control being implemented. Examples are shown to demonstrate the stabilization and identification for linear time invariant and periodic systems with a single control time delay.