On the robustness of linear stabilizing feedback control for linear uncertain systems |
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| Authors: | H. L. Stalford C. H. Chao |
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| Affiliation: | (1) Interdisciplinary Center of Applied Mathematics and Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia;(2) Present address: School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia;(3) Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia;(4) Present address: Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China |
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| Abstract: | ![]()
We investigate linear time-invariant scalar-input systems with constant uncertainties that are not required to satisfy matching conditions. In a previous paper, the existence of stabilizing discontinuous controllers is established under three assumptions for such systems. The first assumption requires controllability of the system for each uncertainty. The second is a condition on an uncertain Lyapunov equation, and the third is a boundedness condition related to the controllability matrix. In this paper, using the same assumptions, we show the existence of a linear stabilizing control. Our result is related to the high-gain theorem of classical control. |
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| Keywords: | Robust control uncertain systems Lyapunov's method linear stabilizing control |
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