Local stability properties of systems with saturation and deadzone nonlinearities

This paper considers the local stability of systems comprising linear time-invariant operators in combination with a deadzone nonlinearity. The behaviour of systems which are not globally bounded-input boundedoutput stable is investigated, and it is shown that under certain conditions, such systems are bounded-output stable for a restricted class of inputs. A sufficient condition for this property is stated as a simple norm inequality, and the restricted input class is shown to be characterised by the energy of the signal. The applicability of this work to systems with saturation nonlinearity, and in particular the well-known “anti-windup” problem is shown, and an example given.