New estimates of upper bounds for the solutions of the continuous algebraic Riccati equation and the redundant control inputs problems

摘要

In this paper, according to the properties of the given matrix of the continuous algebraic Riccati equation (CARE), a new positive semi-definite matrix is constructed. And then basing on some significant properties of the matrix eigenvalue and eigenvalue inequality, using inequality techniques and formula transformation and the new positive semi-definite matrix, a class of new upper bounds of the CARE is obtained. Consequently, in redundant control inputs system, by the derived bounds, inequality techniques, and the important property of the matrix eigenvalue and singular value, we present some new sufficient conditions to guarantee the decrease of controller gain when increasing the control input, which are more adaptable than previous results. Finally, we show the effectiveness of the results by numerical examples. (C) 2020 Elsevier Ltd. All rights reserved.