Interval observers for continuous-time bilinear systems with discrete-time outputs

For a family of continuous-time nonlinear systems with input, output and disturbances in the case where measurements are available only at discrete instants, a new interval observer design is proposed. The family covers bilinear (and linear) systems with static output feedback as special cases. Employing the structure of Luenberger-type observers, we construct framers that allow us to determine a lower and an upper bounds of state variables in the presence of disturbances, provided that intervals in which uncertain initial conditions and uncertain disturbances lie are known. It is proved that the lower and upper bounds of state variables converge to each other completely when the maximum time interval of measurements is sufficiently small in the absence of disturbances.