Robust pole placement by static output feedback

This paper tackles the problem of pole placement by static output feedback. The considered systems are LTI and subject to both polytopic and norm-bounded uncertainties i.e. the uncertain closed-loop state matrix can be written A_o = A + BK_oC + JEL. Matrices A,B,C, J and L belong to polytopes of matrices whereas E is unknown. K_o is the matrix associated with the static output feedback. It is aimed to compute K_o so as to place the spectrum of A_o in an εεMI-region, denoted by D_U, while maximizing the acceptable 2-norm of E ensuring the D_U-stability of A_o. Nevertheless, the pole placement by static output feedback presents two major difficulties: (a) the strict pole placement by static output feedback is usually possible only if Kimura´s condition holds; (b) the non strict pole placement methods through Lyapunov based approaches leads to non convex problems such as BMI (bilinear matrix inequality) rather than LMI (linear matrix inequality). This paper proposes a heuristic technique to compute K_o. It aims at circumventing the difficulties mentioned here before. This technique is based on genetic algorithms (not detailed here) and on the resolution of LMI.