A Generalization of the Cauchy‐Schwarz Inequality and Its Application to Stability Analysis of Nonlinear Impulsive Control Systems

Abstract

In this paper, we first present a generalization of the Cauchy-Schwarz inequality. As an application of our result, we obtain a new sufficient condition for the stability of a class of nonlinear impulsive control systems. We end up this note with a numerical example which shows the effectiveness of our method.

Stability Analysis for Nonlinear Impulsive Control System with Uncertainty Factors

“…If the parameter uncertainty Δ A = 0, the condition of ( 9 ) became the result of Theorem 3.1 in reference [ 30 ]. Thus, the proposed method is a generalization of Peng's method.…”

“…Cauchy–Schwarz inequality is an important tool to study nonlinear systems [ 28 – 31 ]. Recently, Peng et al generalize the Cauchy–Schwarz inequality, which is used to deduce asymptotic stability for a class of nonlinear control systems [ 30 ]. Under the assumption U ( k , x ) = BCx , they study the after nonlinear system: where B and C are constant matrixes.…”