Measures of Overshoot, Speed of Response and Robustness

Performance measures for a class of nonlinear discrete-time system are defined in terms of the eigenvalues and the eigenvectors of the linearized system matrix and an interactive computer-aided design of controller parameters is given. The overshoot and the speed of response are the parameters of an exponential envelope constraining the norm of the states under initial condition perturbations. The robustness is shown to be related to these measures. An interactive computer-aided design is proposed which consists of selecting a controller which yields a `small overshoot´ and `a large speed of response´ measures of the linearized closed loop system.