On companion systems with state saturation nonlinearity

This brief studies the problem of how to check whether a discrete-time companion system with state saturation nonlinearity is free from overflow oscillations or not. The necessary and sufficient condition for the absence of overflow oscillations is established, and the condition is found to be equivalent to the existence of a polyhedral Lyapunov function absorbing state saturation nonlinearity. In this connection, it is stressed that the use of quadratic Lyapunov functions has its limitations in the overflow oscillation analysis. A special topic concerned with Enestrom-Kakeya polynomials is discussed as well.