The analysis of the dynamic equilibrium in nonlinear control system

This paper discusses not a point of equilibrium to free system, but a certain family of equilibrium of nonlinear dynamical system with inputs. This equilibrium depends on the input, so it is called the dynamic equilibrium. The expression of the dynamic equilibrium is given under some certain condition. The stability property of the dynamic equilibrium depends also on the input, and it is discussed in systems with slowly varying input by two methods. We suggest some applications of this theory in the design of the nonlinear control system, address the direct method of feedback linearization based on the dynamic equilibrium state theory and the backstepping technique based on the dynamic equilibrium state theory