Application of a multiplier method to uncertain Lur’e-like systems

This paper investigates the conditions under which an abstract matrix multiplier method can be applied to determine guaranteeing cost controls for systems containing nonlinear/uncertain elements via linear matrix inequalities (LMIs). Quadratically constrained uncertainties and nonlinearities are considered, which comprehend the cases of norm-bounded, positive-real and sector-bounded uncertainties/nonlinearities. Both the discrete-time and the continuous-time cases are discussed. Necessary and sufficient conditions are formulated in the case of unstructured uncertainty. The conditions are sufficient in the structured case. The cost guaranteeing controls can be determined by solving LMIs. Numerical examples illustrate the effectiveness of the proposed method.