The Application of Z-Transform Theory to the Analysis of Switched-Type Nonlinear Systems

The stability of certain discontinuous feedback systems is analyzed by using the z-transform theory. In the z plane, a system which is equivalent to the nonlinear system under steady-state conditions can be found, as well as the existence of any limit cycle, together with the frequency at which it occurs. An intuitive argument for the stability of a limit cycle is also presented, several examples are worked, and the results compared with those obtained by other methods. The z-transform method is exact and is not restricted by the order of the system.