Extended affine bessel summation inequalities: Applications to stability analysis of linear discrete-time systems with time-varying delays

Abstract

This paper concerns the stability analysis problems of linear discrete-time systems with time-varying delays. For developing less conservative stability criteria obtained with the Lyapunov-Krsoavkii approach, numerous Lyapunov-Krasovskii functional (LKF) have been constructed by utilizing various summation quadratic functions. Thus, summation inequalities have been essential methods to develop convex stability criteria which guarantee the negative forward difference of LKFs. To further reduce the conservatism of stability criteria, this paper proposes extended affine Bessel summation inequalities. The proposed summation inequalities provide affine upper bounds of an extended summation quadratic function that contains a systems state variable, its forward difference, and their correlated terms. Further, this paper provides notes on the correlation among several summation inequalities including the proposed ones. These notes also prove that an increase in the degree of the developed affine Bessel summation inequalities only reduces conservatism. Two numerical examples effectively demonstrate the reduction of the conservatism due to the proposed summation inequalities in terms of stability regions which are expressed as delay bounds.(c) 2023 Elsevier Inc. All rights reserved.