Krener's theorem is a result in the field of control theory, particularly relating to the behavior of nonlinear dynamical systems. The theorem is primarily concerned with the existence of optimal control strategies for certain types of control problems. In essence, Krener's theorem provides conditions under which a feedback control law can be formulated that stabilizes a nonlinear system around an equilibrium point and achieves optimality regarding a given performance criterion, typically expressed as a cost function.
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