Eigenvalue assignment for positive observers and its feasibility

In this paper, we discuss a new problem of establishing feasibility conditions for regional eigenvalue assignment of positive observers. Previous results on regional eigenvalue assignment for observers of linear time-invariant positive systems are also improved. Unlike observable dynamical systems whose closed-loop eigenvalues can be assigned arbitrarily, eigenvalues of positive observers are indicated unable to be assigned into any arbitrary region. We derive feasibility conditions in the form of constrained convex programming under which the regional eigenvalue assignment is possible. Moreover, we propose a new method for solving the regional eigenvalue problem of positive observers once the feasibility conditions are satisfied. Numerical examples are given to show the efficacy of the proposed method.