A Polynomial Matrix Inequality approach for zonotopic set-membership estimation of multivariable systems

This paper proposes a methodology for guaranteed state estimation of multivariable linear discrete time systems in the presence of bounded disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed based on the minimization of the P-radius associated to the zonotope. The proposed method leads to an off-line Polynomial Matrix Inequality (PMI) optimization problem. A sub-optimal solution of this problem is obtained using relaxation techniques. An illustrative example is analyzed in order to highlight the performance of the proposed algorithm.