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In setpoint control, an equilibrium of the system to be controlled is typically employed as the setpoint. Thus, it is important to know the “possible equilibria” of the system, i.e. the value at which the state continues to stay by a suitable control input. Here, a possible equilibrium is called a  controllable equilibrium . In this paper, we study two problems on controllable equilibria. First, we consider the problem of determining the set of controllable equilibria associated with constant inputs of magnitude one or less. Second, we address the problem of finding a constant input minimizing the distance between the resulting equilibrium and the desired state value. For each problem, we provide solutions in model-based and data-driven manners.

Equilibrium controllability analysis and input design of linear systems