A New Method with Guaranteed Stability for Discretization of Continuous-Time Control Systems

This paper introduces a new method, called the Plant-Input-Mapping (PIM) method, for discretization of continuous-time control systems (CTCS). In this method a sampled-data control system (SDCS) is designed such that the control input of the SDCS approaches that of the CTCS as the sampling frequency is increased and the stability of the SDCS is guaranteed for any nonpathological sampling period (i.e., when the sampling frequency is not a multiple initegral of the unstable natural frequencies, if any, of the plant). The original CTCS need not be unity feedback and the plant and controller(S) can be unstable and even nonminimum phase. Furthermore. the method can cover any standard hold element used in the discretized system. As far as the authors are aware, such a generality is not provided by any of the discretization methods currently available. In this paper, the method is described for SISO plants but its extension for MIMO plants is straightforward.