Generalized asymptotic regulation with guaranteed H2H2 performance: An LMI solution

A multi-objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix. The generalized regulation constraints are expressed as bounds on the state-steady peak in response to disturbances generated by an anti-stable autonomous exogenous system with nonzero initial states. The controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices, which are subject to convex constraints, and an accompanying controller with which the feedback loop is to be stabilized. Formulating the design of the accompanying controller in a way to guarantee the additional performance objective, the overall design is rendered tractable over a set of free variables, in terms of which the synthesis of a suitable controller is also outlined. The order of the controller is equal to the order of the plant plus the order of the exogenous system. By an adaptation of the developed techniques, a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response.