<p>This work addresses the fixed-time stability (FXTS) problem of nonlinear impulsive systems (NISs) with time-varying parametric uncertainties in the presence of destabilizing impulses. Sufficient conditions for FXTS of NISs with parametric uncertainties are derived using the Lyapunov–Krasovskii functional method in the context of the linear matrix inequality approach. In the context of impulsive system with destabilizing impulses, the assumption of boundedness of parametric uncertainties is significant for the stability analysis of the NISs. Additionally, some novel control schemes are developed including the nonlinear controller with impulsive effects and impulse-dependent settling time (ST) estimation is formulated, accounting for destabilizing impulses. The proposed controllers consist of three components: one to stabilize the impulsive delayed system in the sense of Lyapunov, another to ensure finite-time stability, and the last to achieve FXTS. The proposed findings demonstrate a relation between the impact of impulses and the maximum ST, showing that destabilizing impulses can raise this upper bound and decelerate the system’s convergence rate. Finally, two numerical examples are provided to validate the proposed theoretical results.</p>

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Fixed-time stability of nonlinear systems with time-varying parametric uncertainties under destabilizing impulses

  • Jayabharathi Jayavel,
  • Lakshmanan Shanmugam

摘要

This work addresses the fixed-time stability (FXTS) problem of nonlinear impulsive systems (NISs) with time-varying parametric uncertainties in the presence of destabilizing impulses. Sufficient conditions for FXTS of NISs with parametric uncertainties are derived using the Lyapunov–Krasovskii functional method in the context of the linear matrix inequality approach. In the context of impulsive system with destabilizing impulses, the assumption of boundedness of parametric uncertainties is significant for the stability analysis of the NISs. Additionally, some novel control schemes are developed including the nonlinear controller with impulsive effects and impulse-dependent settling time (ST) estimation is formulated, accounting for destabilizing impulses. The proposed controllers consist of three components: one to stabilize the impulsive delayed system in the sense of Lyapunov, another to ensure finite-time stability, and the last to achieve FXTS. The proposed findings demonstrate a relation between the impact of impulses and the maximum ST, showing that destabilizing impulses can raise this upper bound and decelerate the system’s convergence rate. Finally, two numerical examples are provided to validate the proposed theoretical results.