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

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.