Tight robust interval observers: An LP approach

This paper provides a solution based on linear programming to the problem of designing observers that ensures guaranteed bounds on the estimated states. Firstly, considering linear systems without uncertainties, we provide a complete solution for the existence of interval observers having minimal l₁-norm of the interval error. Secondly, new type of observers involving dilatation functions, are introduced in order to deal with the robust estimation of systems that are possibly nonlinear and subject to uncertainties. A new methodology is provided for the design and characterization of tight robust interval observers. All the proposed conditions are expressed in term of linear programming.