Resumen de Second-order counterexamples to the discrete-time Kalman conjecture

William Paul Heath, Joaquín Carrasco, Manuel de la Sen Parte

• The Kalman conjecture is known to be true for third-order continuous-time systems. We show that it is false in general for second-order discrete-time systems by construction of counterexamples with stable periodic solutions. We discuss a class of second-order discrete-time systems for which it is true provided the nonlinearity is odd, but false in general. This has strong implications for the analysis of saturated systems.