Dwell-time stability conditions for infinite dimensional impulsive systems

Article Automation & Control Systems

ISS and integral-ISS of switched systems with nonlinear supply functions

Shenyu Liu et al.

Summary: This paper investigates the input-to-state stability (ISS) and integral version (iISS) of switched nonlinear systems with inputs, resets, and possibly unstable subsystems. By utilizing dissipation inequalities, supply functions, and the change in Lyapunov functions at switching instants, a formula relating average dwell-time (ADT) and average activation time (AAT) is derived to ensure the stability of the switched system. Case studies are included to illustrate the results.

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS (2022)

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Article Automation & Control Systems

Stability conditions for impulsive dynamical systems

Sergey Dashkovskiy et al.

Summary: This work investigates the stability conditions of impulsive dynamical systems evolving on an infinite-dimensional space and under external perturbations. New dwell-time conditions are proposed to handle situations where both continuous and discrete dynamics can be unstable simultaneously, with Lyapunov-like methods developed for this purpose. Finite and infinite dimensional examples are provided to demonstrate the application and effectiveness of the main results, which cannot be addressed by any other existing approaches.

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS (2022)

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Article Mathematics, Applied

Eigenvalues and delay differential equations: periodic coefficients, impulses and rigorous numerics

Kevin E. M. Church

Summary: This study introduces validated numerical methods for computing Floquet multipliers of delay differential equations, demonstrating its efficacy through computer-assisted proofs and testing on example problems. By representing the monodromy operator as an operator acting on sequence spaces, and carefully bounding truncation errors, the method is suitable for rigorously counting the number of Floquet multipliers outside a closed disc centered at zero or contained in a compact set bounded away from zero.

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2021)

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Article Automation & Control Systems