Stability of impulsive systems depending on a parameter

Abstract

In this paper, we present a practical exponential stability result for impulsive dynamic systems depending on a parameter. Stability theorem and converse stability theorem are established by employing the second Lyapunov method. These theorems are used to analyze the practical exponential stability of the solution of perturbed impulsive systems and cascaded impulsive systems, depending on a parameter. Copyright © 2015 John Wiley & Sons, Ltd.

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

“…Ideas analogous to those employed in the proof of Theorem 3.1 could also be employed to derive results when the decaying term converges in finite-time [47] or is exponential [48]. Moreover, the two-measure framework can be employed when stability is only practical [49].…”

Partial practical stability for fractional‐order nonlinear systems

“…In addition, Gallegos et al 12 have introduced a smooth solutions to the mixed‐order fractional differential systems with applications to stability analysis. Furthermore, Ghanmi 13 studied the results of the practical exponential stability of impulsive nonlinear systems depending on a parameter. The practical stability has some applications in real‐world applications, which is also introduced in previous work.…”

“…Analogical to the qualitative particular of the non-integer and fractional differential equations, the generation of the Lyapunov theory, fixed point theory, and the Mittag-Leffler function allows to construct many and remarkable results in the stability, the exponential stability, and the Mittag-Leffler stability. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Indeed, Ben Hamed et al 5 have studied a converse Lyapunov theorem for the notion of uniform practical exponential stability of parametric differential equations in presence of small perturbation. Ben Makhlouf 6 has described the stability with respect to part of the variables of nonlinear Caputo fractional differential equations.…”

Robust control for uncertain impulsive systems with input constraints and external disturbance

“…Luo et al 10 presented a general framework for analyzing stability of linear impulsive systems, but there was not much discussion of external disturbances. Ghanmi 11 provided sufficient and necessary conditions to ensure the practical exponential stability of nonlinear impulsive systems, and these results were interestingly applied to perturbed systems, as well as to the special cases of the cascaded systems. The problems of input-state stability, dissipativity, and H ∞ control for switched/impulsive systems with external disturbances have been investigated.…”