On the global polynomial stabilization and observation with optimal decay rate

New investigations in the problems of polynomial stabilization are presented in this paper, where some relaxed results related to homogeneity theory leading to this polynomial stability with optimal decay rate are developed. To achieve our analysis, several physical examples are presented showing how we can construct stabilizing feedback laws making these closed loop systems polynomially stable with op-timal decay rates. This allows the redesign of (a) homogeneous feedbacks stabilizing polynomially the Heisenberg system in weak sense, (b) and the polynomial observer for the angular momentum satellite with one control input. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates polynomial stabilization problems and develops relaxed results related to homogeneity theory. It presents several physical examples to show how stabilizing feedback laws can be constructed to achieve polynomial stability with optimal decay rates in closed loop systems.