Simultaneous pole placement of M discrete-time plants using a M-periodic controller

A generic procedure for designing a M-periodic controller (sought in the controller canonical form) for the simultaneous placement of the closed-loop poles of M (=2,3,4,...) discrete, time-invariant plants is presented. The procedure is a two-stage one: first, a set of M simultaneous, linear, polynomial equations, arising out of the M given plants and the corresponding desired closed-loop pole locations, are solved via a generalized Sylvester matrix approach to obtain a set of (M+1) intermediate polynomials; and next, the controller parameters are obtained solving another set of simultaneous, linear polynomial equations that involve the above intermediate polynomials. Thus, both the computational steps are linear algebraic in nature. A list of the isolated plant configurations for which solutions do not exist is given. An example illustrates the procedure.