Parameterized linear systems and linearization families for nonlinear systems

The question of characterizing parameterized linear systems that can arise as linearization families of a nonlinear system about a family of constant operating points is addressed. The parameterization can be in terms of operating-point inputs or operating-point outputs. For both parameterized linear state equations and parameterized transfer functions, existence conditions, and constructions, for a corresponding nonlinear system are presented.