New Interesting Facts About Minimum-Energy Perfect Control for LTI Nonsquare State-Space Systems

In this paper a breakthrough in the area of the minimum-energy perfect control for discrete-time state-space systems with different number of input and output variables is presented. Following the recently performed heuristic simulation studies corresponding to mentioned control strategy, the analytical confirmation is presented through this paper. Up to now, the statement that the so-called right sigma-inverse clearly outperforms the minimum-norm (T-) inverse in terms of minimum-energy of the MV/perfect control inputs design has been based on optimization tasks only. Therefore, the heuristic studies made in Matlab environment could not be treated as the representative ones in some sense, so far. Simple analytical illustrative example shows the big minimum-energy applicability of sigma-inverse over usage of classical minimum-norm one. Note that full proof is not given yet and still waiting for deep exploration.