LMI approach to digital redesign of linear time-invariant systems

A simple and new design methodology for the digital redesign of static state feedback controllers by using linear matrix inequalities is presented. The proposed method provides close matching of the states between the original continuous-time system and those of the digitally redesigned system with a guaranteed stability. Specifically, the digital redesign problem is reformulated as linear matrix inequalities (LMIs) and solved by the efficient numerical optimisation technique. The main feature of the proposed method is that the closed-loop stability of the digitally redesigned system is explicitly guaranteed within the design procedure using the LMI-based approach. A numerical example of the position control of a simple crane system is presented.