Pole-free perfect control for nonsquare LTI discrete-time systems with two state variables

In this paper a new method concerning the problem of pole-free perfect control for discrete-time LTI nonsquare systems is presented. It is shown that application of a-inverse of parameter matrix into the process of designing the above mentioned control strategy can be useful for nonsquare systems, i.e. systems comprising different numbers of input and output variables. Thus, the special selected so-called degrees of freedom of a-inverse contribute to more robust pole-free perfect control. Notwithstanding, the proposed approach can only be used for second-order systems, thus giving rise to develop the research effort for more complex systems in the future. Simulation examples made in Matlab environment confirm the big potential of a new analytical pole-free perfect control solution corresponding to the well-known pole placement problem.