Time‐dependent Luenberger‐type interval observer design for uncertain time‐varying systems

Abstract This article investigates the state interval observation problem for a class of continuous and discrete‐time linear time‐varying (LTV) systems with bounded uncertainties separately. First, by utilizing both the LTV transformation and the solutions to a type of time‐varying fully‐actuated Sylvester equations, a time‐dependent standard interval observer (IO) is established in a parametric form with some design degrees of freedom. Second, a new time‐dependent structure of Luenberger‐type IOs is proposed to relax the limitation of the LTV transformation‐based design method. Further, its sufficient existence conditions are given in virtue of positive system theory. Meanwhile, a parametric design technique of such an IO for uncertain LTV systems is also raised under rank conditions. Third, the obtained results are extended to the discrete‐time systems. Finally, the correctness and benefits of the proposed methods are verified using some numerical examples.