Robust Delay-Independent/Dependent Stabilization of Uncertain Time-Delay Systems by Variable Structure Control

It is well known that many engineering control systems such as conventional oil-chemical industrial processes, nuclear reactors, long transmission lines in pneumatic, hydraulic and rolling mill systems, flexible joint robotic manipulators and machine-tool systems, jet engine and automobile control, human-autopilot systems, ground controlled satellite and networked control and communication systems, space autopilot and missile-guidance systems, etc. contain some time-delay effects, model uncertainties and external disturbances. These processes and plants can be modeled by some uncertain dynamical systems with state and input delays. The existence of time-delay effects is frequently a source of instability and it degrades the control performances. The stabilization of systems with time-delay is not easier than that of systems without time-delay. Therefore, the stability analysis and controller design for uncertain systems with delay are important both in theory and in practice. The problem of robust stabilization of uncertain time-delay systems by various types of controllers such as PID controller, Smith predictor, and time-delay controller, recently, sliding mode controllers have received considerable attention of researchers. However, in contrast to variable structure systems without time-delay, there is relatively no large number of papers concerning the sliding mode control of time-delay systems. Generally, stability analysis can be divided into two categories: delay-independent and delay-dependent. It is worth to mention that delay-dependent conditions are less conservative than delay-independent ones because of using the information on the size of delays, especially when time-delays are small. As known from (Utkin, 1977)-(Jafarov, 2009) etc. sliding mode control has several useful advantages, e.g. fast response, good transient performance, and robustness to the plant parameter variations and external disturbances. For this reason, now, sliding mode control is considered as an efficient tool to design of robust controllers for stabilization of complex systems with parameter perturbations and external disturbances. Some new problems of the sliding mode control of time-delay systems have been addressed in papers (Shyu & Yan, 1993)-(Jafarov, 2005). Shyu and Yan (Shyu & Yan, 1993) have established a new sufficient condition to guarantee the robust stability and β-stability for uncertain systems with single time-delay. By these conditions a variable structure controller is designed to stabilize the time-delay systems with uncertainties. Koshkoei and Zinober (Koshkouei & Zinober, 1996) have designed a new