Digital interval modeling and hybrid control of uncertain systems

Abstract

This paper addresses two issues: (1) converting a continuous-time uncertain system to an equivalent discrete-time interval model; and (2) constructing a robust digital control law from a robust analogue control law for hybrid control of sampled-data uncertain systems. The system matrices characterizing the state-space representation of the original continuous-time uncertain systems are assumed to be interval matrices. The Pade approximation method together with a geometric-series approximation method is employed to obtain the generalized enclosing discrete-time interval models. The generalized enclosing interval models are able to tightly enclose the exact discrete-time uncertain model, and can be utilized for digital simulation and digital design of continuous-time uncertain systems. A new family of digitally redesigned interval controllers is constructed from a continuous-time robust controller for robust digital control of continuous-time uncertain systems. Using the newly digitally redesigned interval controllers, the dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.