Bounded real property of time-delay time-varying systems and its application to learning control

Bounded real condition for time-delay time-varying (TDTV) systems are derived using delay deferential state space equations. Using this result stability conditions for learning control of time-delay time-varying systems are discussed. The error of learning control converges to zero by increasing the number of the trials if the corresponding error transition system is bounded real. The paper is organized as follows. In section 1 the authors introduce the state space equation of TDTV systems and the definition of bounded real condition for TDTV systems. In section 2 the authors give the stability condition of the learning control system for TDTV systems based on the BR condition for TDTV systems. In the final section the authors show numerical examples of TDTV systems using MATLAB