Static feedback design for 2D mixed continuous-discrete-time systems via LMIs

This paper addresses the problem of designing static feedback controllers for 2D mixed continuous-discrete-time systems via linear matrix inequalities (LMIs). It is shown that a necessary and sufficient condition can be obtained by solving two LMI problems. The first LMI problem aims at determining a polynomial whose positivity domain corresponds to stabilizing controllers. The second LMI problem aims at identifying one controller in such a domain. The condition is sufficient for any size of the LMI problems, and is necessary for a sufficiently large one. Some numerical examples illustrate the proposed methodology.