Systems with Monotone and Slope Restricted Nonlinearities

Abstract

The paper starts from the suggestion of R. E. Kalman that additional information
on nonlinearity slope may improve the sufficient conditions for absolute stability. This
leads to the so called systems with augmented dynamics. Motivated also by the problem of
the PIO II aircraft oscillations - self sustained oscillations induced by the saturation nonlinearities,
which are both sector and slope restricted - the paper considers a generalization of
the Yakubovich criterion to the case of the systems with critical and unstable linear part. The
same generalization concerns a quite well known stability criterion where only slope restrictions
are taken into account: the published version is improved by using all advantages of the
Liapunov method and of the frequency domain stability inequalities. The results are illustrated
by several applications.