Switched systems approach to state bounding for time delay systems (Q2200536)

A linear discrete-time system with time-varying delay is considered in the presence of bounded peak disturbances. This system is transformed into a switched delay-free system by augmentation of the state variables. The switching signal of the obtained switched system is determined by the time delay. The number of decision variables in the obtained reachable set estimation condition is small compared with the Lyapunov-Krasovskii functional method. Also, the problem of mean square estimation of the system state is studied for the case of random delay. By using the same augmentation technique, the random delay system is transformed into a delay-free Markov jump system and two estimates of the corresponding reachable set are obtained. Simulation examples illustrate the proposed approach.