ON CLASSICAL STATE SPACE REALIZABILITY OF QUADRATIC INPUT-OUTPUT DIFFERENTIAL EQUATIONS

This paper studies the realizability property of continuous-time quadratic input-output (i/o) equations in the classical state space form. Constraints on the parameters of the quadratic i/o model are suggested that lead to realizable models. The complete list of 2nd and 3rd order realizable i/o quadratic models is given and two subclasses of the nth order realizable i/o quadratic systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit state equations for realizable 2nd order quadratic i/o equations, and for one realizable subclass of quadratic i/o equations of arbitrary order.