Year: 2026
Type: article
Abstract: An infinite-horizon H∞ linear-quadratic control problem is considered. This problem has the following features: (i) the control cost in the cost functional has a positive small coefficient (small parameter), meaning that the control cost is much smaller than the state cost; (ii) the current cost of the fast state variable in the cost functional is a non-zero positive semi-definite quadratic form. These features require developing a significantly novel approach to asymptotic analysis of the matrix Riccati algebraic equation appearing in the solvability conditions of the considered H∞ problem. Using this solution, an asymptotic analysis of the H∞ problem is carried out. This analysis yields parameter-free solvability conditions for this problem and a simplified controller solving this problem. An example illustrating the theoretical results is presented.
Source: Axioms
Authors: Valery Y. Glizer, Vladimir Turetsky
Institution: Braude College of Engineering Karmiel
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7125830114
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