Robust PI observer design for hybrid heterogeneous multiple models with delayed measurements

This paper deals with the problem of state estimation for hybrid systems modelled via multiple models and subject to delayed measurements. In contrast to the most popular results found in the multiple model literature, we consider heterogeneous multiple models, also known as decoupled multiple model, which allow to use submodels whose state space dimension can be different. On the basis of this multiple model a proportional-integral observer (PIO) is designed in order to cope with the robust state estimation with respect to disturbances. Sufficient delay-independent conditions for ensuring robust performances (attenuation level) and dynamic performances (exponential convergence) of the estimation error are provided in terms of LMIs using the Lyapunov-Krasovskii method. The validity of the proposed methodology is illustrated by an academic example.