Digital redesign of H_∞ controller via bilinear approximation method for state-delayed systems

Two issues are addressed: digitial modeling of the continuous-time state-delayed system; and digital redesign of the observer-based H_∞ controller for the continuous-time state-delayed system. The bilinear approximation method together with the linear interpolation is utilized to find an equivalent discrete-time model of the original continuous-time state-delayed system, so that the states of the obtained discrete-time model closely match those of the original continuous-time statedelayed system. In addition, the same idea is used to establish an equivalent digital controller from the analogue H_∞ controller for the continuous-time state-delayed system, so that the states of the digitally controlled sampled-data state-delayed system closely match those of the original analogously controlled continuoustime state-delayed system. A discrete-time observer is constructed from the original continuous-time observer via a modified lifting technique, such that the estimated states of the obtained discrete-time observer match those of the original continuous-time observer at the sampling instants. Using the newly digitally redesigned observer-based controllers, the resulting dynamic states of the overall digitally controlled sampled-data state-delayed systems are able to closely match those of the original observer-based analogously controlled continuous-time state-delayed systems. An illustrative example is given to show the digital modeling and digital redesign results for a state-delayed system.