Observability of C ^∞-systems for L ^∞-single-inputs and some examples

Abstract

For single-input multi-outputs C ^∞-systems conditions under which observability for every C ^∞ input implies observability for every almost everywhere continuous, bounded input (for every L ^∞ input in the control-affine case) are stated. A normal system is then defined as a system whose only bad inputs are smooth on some open subset of definition. When the state space is compat normality turns out to be generic and enables to extend some results of genericity of observability to nonsmooth inputs.