State estimation and control of nonlinear systems with large and variable measurement delays Filippo Cacace, Alfredo Germani and Costanzo Manes Abstract We investigate the problem of extending the classical approach to nonlin- ear control, based on state estimation and state feedback, to the case of systems affected by time-varying measurement delay. We show that it is possible to de- sign globally exponentially convergent high-gain observers based on a a linearizing change of coordinates that, under sufficient conditions that are similar to the non delayed case, allow to control the system. We also derive sufficient conditions for the global regulation of the system by means of nonlinear state feedback using the estimate provided by the observer, in analogy with the separation theorem. The main limitation is the presence of a delay bound that depends on the Lipschitz constant of the nonlinear system. To overcome this limitation it is possible to resort to a chain of observers that, at the cost of a growing realization space and convergence time, can in principle allow to compensate any delay. This design is straightforward when the delay is known and constant but its extension to time-varying delays requires spe- cial attention, in particular when the delay is not continuous with respect to time, as it frequently happens in the applications. We therefore introduce a classification of delay functions with respect to the available output information and illustrate how to design the cascade of elementary observers to solve the state reconstruction prob- lem. We also characterize the class of delay functions for which this approach fails to provide a viable implementation. Filippo Cacace Universit` a Campus Biomedico di Roma, e-mail: f.cacace@unicampus.it Alfredo Germani and Costanzo Manes Universit` a dell’Aquila, e-mail: alfredo.germani@univaq.it,costanzo.manes@ univaq.it 1