Quadratic-in-the-state representation of nonlinear systems via immersion

This paper considers quadratic-in-the-state representations which consist of state equations that are at most quadratic with respect to the states, as representations for a broad class of nonlinear systems. A necessary and sufficient condition is shown for existence of a quadratic-in-the-state representation that has the identical input-output relation with a given nonlinear system. The condition is so moderate that many types of nonlinear systems can be represented with a state equation that is at most quadratic with respect to the states. The quadratic-in-the-state representation is expected to be useful as a general model structure in identification of nonlinear systems