Stabilization of discrete-time systems with time-varying delay using simple lyapunov-krasovskii functional

Abstract

This thesis studies stabilization of discrete time-delay systems based on Lyapunov-Krasovskii functional. Time-delays frequently occur in various practical systems, such as networked control systems, chemical processes, neural networks, and long transmission lines in pneumatic systems. The different phenomena that cause time-delay are: (a) Time needed to transport mass, energy or information; (b) Time lags get accumulated in great number of low-order systems connected in series; and (c) Sensors, such as analyzers; controllers need some time to implement a complicated control algorithm or process. The presence of delay causes in general performance degradation and may lead to instability within the system First, stability of networked control systems has been studied. Two available stability criteria for linear discrete time systems with interval like time varying delay have been considered. Also a numerical example has been solved and the results of both the stability criteria have been compared. Static output-feedback stabilization of discrete-time system with time-varying delay is studied next. Two stabilization approaches based on the above discussed stability criteria are studied. A numerical example has been solved and simulation results have been obtained for both the approaches. Simulation output indicates that the given stabilization approaches effectively stabilize the system and their performance in terms of achievable delay margin is compared.