Interval observer estimation and predictive control for a biotechnological system

Robust $H_{\infty}$ Interval Observer for Linear Systems With a Controllable Convergence Rate: A Parametric Method

“…Step 5: Denote a Metzler and Hurwitz matrix M and a non-singular matrix T , then a transformed system is obtained as (17). Go to Step 6.…”

“…Therefore, because of its great breakthrough in structure and the unique treatment of uncertainties, the interval observers become one of the research hotspots in observer theory recently. After introduced by J. L. Gouzé in [15] and wildly applied to the biological positive systems [16], [17], the interval observers attract the considerable interest of researchers.…”

Functional interval observer for the linear systems with disturbances

“…However, distinguishing from above, the uncertainties are considered in the process of designing interval observer, and because of its great inclusiveness to the disturbances, the interval observer as the powerful complement of observer theory has the advantages of uncomplicated design method and easy physical realisation, comparing with existing design methods of the observers for the complex systems. After first introduced by Gouze in [21] and applied widely to biological systems [21–23], the interval observer attracts the considerable interest of researchers in the control theory. Utilising the characteristic of the positive systems, where its state trajectory is determined by the initial value and input of the systems, the observation for the states of the systems is achieved by a dynamic system which provides the upper and lower bounds of the estimated states.…”