Set-membership EIV identification through LMI relaxation techniques

Abstract — In this paper the Set-membership Error-In-Variables (EIV) identification problem is considered, that is the identification of linear dynamic systems when both the output and the input measurements are corrupted by bounded noise. A new approach for the computation of the Parameters Uncertainty Intervals (PUIs) is discussed. First the problem is formulated in terms of non-convex semi-algebraic optimization. Then, a Linear-Matrix-Inequalities relaxation technique is pre-sented to compute parameters bounds by means of convex op-timization. Finally, convergence properties and computational complexity of the given algorithms are discussed. Advantages of the proposed technique with respect to previously published ones are discussed both theoretically and by means of a simulated example. Index Terms — Set-membership identification, errors-in-variables, LMI relaxation