Asymptotic stability analysis and design of nonlinear impulsive control systems

Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

“…In the next section, we employ Theorem 3.1 in order to generalize several existing results. Comparison-type results have been recently employed in [46] for impulsive systems with no inputs and in [13] for impulsive (switched) systems with inputs. In both papers, the comparison systems are given by impulsive differential equations like (10) instead of by differential/difference inclusions as (7).…”

“…Refs. [13] and [46] require that the functions playing the role of our α λ (t, r) in Assumption 1 be nondecreasing in r. This requirement allows the use of the simpler comparison systems (see Remark 3). Assuming that the functions α λ (t, r) are nondecreasing in r seems a nonnatural and restrictive assumption in a nonlinear context (see Theorems 4.4 and 5.2).…”

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

“…The stability problems of nonlinear impulsive control system (5) have been investigated extensively in the literature in the past several decades. For example, a number of sufficient conditions for the stability of nonlinear impulsive control system (5) are derived in [24][25][26][27]. Inequalities play an important role in their research, for instance, by using the Cauchy-Schwarz inequality [1] and comparison principle [27], and Yang showed a sufficient condition for the stability of nonlinear impulsive control system (5).…”

“…So we want to know whether the angle between and ( ) has an effect on the stability of systems. And the results showed in [24][25][26][27] do not take into account this factor. This is the motivation for the present paper.…”

Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

“…During the last several decades, impulsive control theory has attracted considerable attention because impulsive control method can be employed in many fields, such as the stabilization and synchronization of chaotic systems [11][12][13][14] and complex dynamical networks [15][16][17][18][19]. For more results on impulsive control and its applications, the reader is referred to [11,20,21] and the references therein.…”