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A reliable synthesis of discrete-time Η∞ control. Part I: basic theorems and J-lossless conjugators

Suchomski P. J.

Control and Cybernetics

2007

Vol. 36, no 1

97-141

The paper gives a basis for solving many problems of numerically reliable synthesis of sub-optimal discrete-time control in Η∞. The approach is based on J-lossless factorisations of the delta-domain chain-scattering descriptions of continuous-time plants being controlled. Relevant properties of poles and zeros of chain-scattering models are given. Necessary and sufficient conditions for the existence of stabilising J-lossless conjugators are presented and discussed. Some aspects of numerical conditioning of synthesis of such conjugators are considered. A numerical example illustrating synthesis of stabilising right J-lossless conjugators is also included.