Robust mixed H2/H-infinity control of 2-dimensional systems in Roesser model

The H2 performance specification for one-dimensional systems has been known to be analytically and practically meaningful and widely used in the analysis and design of control and filtering systems. However, it is still of little use in the analysis and design of two-dimensional systems due to the structural and dynamical complexity of two-dimensional systems. In this paper, we extend the classical definition of the H2 performance to two-dimensional systems and present a sufficient condition for evaluation of the H2 performance of two-dimensional systems in Roesser model. Using this condition and the existing bounded real lemma for two-dimensional systems, we develop systematic design methods for mixed H2/H-infinity and robust H2/H-infinity control of two-dimensional systems with polytopic uncertainty. It is worth pointing out that our robust control approach can also be applied to give a solution to the dynamic output feedback control of one-dimensional systems with polytopic uncertainty which has not been solved in existing literature.