Improved Independent and Uniform Multivariable Gain and Phase Margins in \mathcal /LTR Control

• Published in: IEEE transactions on automatic control Vol. 66; no. 10; pp. 4807 - 4811
• Main Authors: Ferreira, Luis H. C., Guaracy, Fernando H. D.
• Format: Journal Article
• Language: English
• Published: IEEE 01-10-2021
• Subjects: <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> mathcal {H}_{\infty }</tex-math> </inline-formula> control; Feedback loop; Frequency-domain analysis; improved stability margins; LQG control; LTR procedure; Numerical stability; Regulators; Robustness; Stability criteria; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3036025

In this article, we presented guaranteed independent and uniform multivariable stability margins for the <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula>/LTR control, both in continuous and discrete time. In previous works, it was shown that the <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula>/LTR control generalizes the linear quadratic Gaussian (LQG)/LTR setup, allowing the designer to better impose bounds on the complementary sensitivity frequency peak in the loop-shaping procedure. In this article, we extend this result by showing that <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula>/LTR control is able to recover better robustness properties than those recovered in the LQG/LTR case. Numerical examples are presented for multivariable and monovariable cases.