Exact observability and exponential stability of infinite-dimensional bilinear systems

This paper deals with exact observability and stability for a class of infinite-dimensional bilinear systems. First we show that the bilinear systems are exactly observable for any positive bounded input signal. Second we prove that given such an input signal the open-loop bilinear systems (or time-varying linear systems) are exponentially stable. A strong motivation of our study comes from chemical engineering processes described by partial differential equations.