A Generalized Framework of Linear Multivariable Control

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Nonstandard H_∞ control problem

A generalized chain-scattering representation approach

Abstract

The nonstandard $H_{\infty }$ control problem is the case where the direct feedthroughs from the input to the error and from the exogenous signal to the output are not necessarily of full rank. This problem is reformulated based on the generalized chain-scattering representation (GCSR). The GCSR approach leads naturally to a generalization of the homographic transformation. The state-space realization for this generalized homographic transformation and a number of fundamental cascade structures of the $H_{\infty }$ control systems are further studied in a unified framework ...