Abstract
We can design nonlinear model following control systems whose inner states are bounded based on the consideration to separate the object system into a linear part and a nonlinear part. In this method zeros of linear part must be stable. It is desirable to remove the condition which is a constraint of design. The stability of an inverse system is concerned with a linear part and a nonlinear part of the original system. From another view point, this fact has the possibility that a closed loop system becomes stable when nonlinear properties satisfy some conditions. By using the property of nonlinear part positively, the whole system can be stable based on stable zero assignment of a linear part. We take the method to set the linear system matrix stable compulsorily and to include an original linear part in a nonlinear part. As the result of this method, a closed loop becomes stable even though zeros of an object system are unstable. The boundedness of internal states can be shown by obtaining a whole dynamic system which includes state variable filters and examining a time derivative of a quadratic form of the whole system. In this proof the assumptions of norms for nonlinear functions, a positive real condition of a transfer function and an inner product of a nonlinear function and a state vector are used. These assumptions are imposed on an object system as the conditions for boundedness of internal states. The parameters of a control law can be selected independent of these assumptions. Especially, in case that the relation of input and output is collocation, a positive real condition is satisfied automatically. Finally we confirm that the design method of this paper is useful by simulating numerical examples.
