Semistabilization, feedback dissipativation, system thermodynamics, and limits of performance in feedback control

In this paper, we develop a thermodynamic framework for semistabilization of linear and nonlinear dynamical systems. The proposed framework unifies system thermodynamic concepts with feedback dissipativity and control theory to provide a thermodynamic-based semistabilization framework for feedback control design. Specifically, we consider feedback passive and dissipative systems since these systems are not only widespread in systems and control, but also have clear connections to thermodynamics. In addition, we define the notion of entropy for a nonlinear feedback dissipative dynamical system. Then, we develop a state feedback control design framework that minimizes the time-averaged system entropy and show that, under certain conditions, this controller also minimizes the time-averaged system energy. The main result is cast as an optimal control problem characterized by an optimization problem involving two linear matrix inequalities.