Equilibratability of Control Systems

In this paper, the problem of moving the equilibrium point of a control system to a desired point or desired space is considered. At the first stage of problem definition, the concept of equilibratability is introduced for the general class of nonlinear systems. Then, necessary and sufficient conditions for equilibratability of linear time-invariant (LTI) systems are investigated for continuous and discrete time scenarios. Next, the problem of input selection based on equilibratability is proposed and investigated. When the input matrix is fixed and the system is not equilibratable at the desired point, an optimization problem is presented to select the nearest equilibratable point. Furthermore, when -instead of equilibrium point- an equilibrium space is sought, two supplementary optimization problems are put forward.