Abstract
Simple state-space formulae are derived for all controllers solving a standard H ∞ problem: for a given number γ≥0, find all controllers such that the H ∞ norm of the closed-loop transfer function is <γ. Under these conditions, a parametrization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable free parameter. The state dimension of the coefficient matrix for the LFT equals that of the plant, and has a separation structure reminiscent of classical LQG (i.e., H 2) theory. Indeed, the whole development is very reminiscent of earlier H 2 results, especially those of Willems (1971). This paper directly generalizes the results in Doyle, Glover, Khargonekar, and Francis, 1989, and Glover and Doyle, 1988. Some aspects of the optimal case (≤γ) are considered.
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Glover, K., Doyle, J.C. (1989). A state space approach to H ∞ optimal control. In: Nijmeijer, H., Schumacher, J.M. (eds) Three Decades of Mathematical System Theory. Lecture Notes in Control and Information Sciences, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008463
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DOI: https://doi.org/10.1007/BFb0008463
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