Optimal reduced-order interval observer design for uncertain continuous-time linear systems

This article investigates the reduced-order interval observer (R-IO) design technique for continuous-time linear systems with unknown external disturbances and measurement noises. First, we propose a coupled R-IO structure with more design degrees of freedom, and it can be directly applied not only to solve the difficulty of the error system cooperativity construction but to relax the constraint on the sensor measurement noises. Second, the R-IO existence condition is derived as a set of matrix equations (MEs), and a complete solution, explicitly showing the available design parameters, to such an R-IO is further obtained by solving the MEs. Third, using the solution, an integrated optimization indicator of the R-IO performance is built as the valid selection mechanism of these parameters. Finally, the efficiency of the obtained results is illustrated through a numerical example and a practical example.