Abstract
For a double integrator subject to input saturation, it is well-known that linear
control laws can achieve global asymptotic stability. But a study of external stability for
such a simple system reveals an unexpectedly rich nature, It is shown in this paper
that external Lp stability for lion-in put-additive disturbance only holds for p ::; 2, but
not for p > 2 no matter what linear control law is used. However, for input-additive
disturbance, Lp stability holds for all 1 ::; p <(Xl, As a third result, we show that the
double integrator system controlled by a saturating linear feedback is not input-to-state
stable (ISS) even when all disturbances have their magnitudes restricted to be arbitrarily
small. These results for the first time reveal t,hat external stability of nonlinear systems
is essentially different from that of linear systems. A fundamental discovery in this study
is that the external stability of nonlinear systems cannot be separated from the internal
state behavior.
| Original language | English |
|---|---|
| Pages (from-to) | 429-451 |
| Journal | Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications & Algorithms |
| Volume | 11 |
| Issue number | 4-5 |
| Publication status | Published - 2004 |