Parameter identification for uncertain linear systems with partial state measurements under an H∞ criterion

The paper addresses the worst-case parameter identification problem for linear systems under partial state measurements. Using the cost-to-come function method, worst-case identifiers are derived for SISO systems. The worst-case identifier thus obtained includes the Kreisselmeier observer as part of its structure, with parameters set at some optimal values. Its structure is different from the common least-squares (LS) identifier, however, in the sense that there is an additional dynamics for the state estimate, coupled with the dynamics of the parameter estimate in a nontrivial way. A reduced-order identifier is obtained, which is numerically much better conditioned when the disturbances in the measurement equations are 'small.'