0c1049f734056e8d4c21001c912cc19e mathematics-13-01157-v2.pdf b2799106d520b26cbf5a1cb4f5754f48cb4a1d07 mathematics-13-01157-v2.pdf e5a95c492f4ab7e983ffe453a5e4b2d5ea08cd3f81bb800904cfdd3b869aa655 mathematics-13-01157-v2.pdf Title: Fixed Points of Self-Mappings with Jumping Effects: Application to Stability of a Class of Impulsive Dynamic Systems Subject: This paper studies the boundedness and convergence properties of the sequences generated by strict and weak contractions in metric spaces, as well as their fixed points, in the event that finite jumps can take place from the left to the right limits of the successive values of the generated sequences. An application is devoted to the stabilization and the asymptotic stabilization of impulsive linear time-varying dynamic systems of the n-th order. The impulses are formalized based on the theory of Dirac distributions. Several results are stated and proved, namely, (a) for the case when the time derivative of the differential system is impulsive at isolated time instants; (b) for the case when the matrix function of dynamics is almost everywhere differentiable with impulsive effects at isolated time instants; and (c) for the case of combinations of the two above effects, which can either jointly take place at the same time instants or at distinct time instants. In the first case, finite discontinuities of the first order in the solution are generated; that is, equivalently, finite jumps take place between the corresponding left and right limits of the solution at the impulsive time instants. The second case generates, equivalently, finite jumps in the first derivative of the solution with respect to time from their left to their right limits at the corresponding impulsive time instants. Finally, the third case exhibits both of the above effects in a combined way. Keywords: impulsive actions; discontinuities of the first kind; dynamic systems; impulsive dynamic systems; global stability; global asymptotic stability; Dirac distribution Author: Manuel De la Sen, Asier Ibeas, Aitor J. Garrido and Izaskun Garrido Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Thu Apr 3 10:36:49 2025 CEST ModDate: Thu Apr 3 10:39:45 2025 CEST Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 40 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 5077910 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- MIKRSI+VnURWPalladioL Type 1 Custom yes yes yes 10 0 BUOMUB+URWPalladioL-Roma Type 1 Custom yes yes yes 16 0 PDCLZL+URWPalladioL-Bold Type 1 Custom yes yes yes 22 0 LLREZA+URWPalladioL-Ital Type 1 Custom yes yes yes 27 0 XELCET+CMEX10 Type 1 Builtin yes yes yes 59 0 SJCXYF+PazoMath-Italic Type 1 Builtin yes yes yes 64 0 VUABVQ+CMMI10 Type 1 Builtin yes yes yes 69 0 SOSTRQ+CMR10 Type 1 Builtin yes yes yes 74 0 UUZGTJ+CMSY10 Type 1 Builtin yes yes yes 79 0 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section.1 Item: Title: Main Results on Distances, Boundedness, and Convergence for Jumping Self-Mappings Destination: section.2 Item: Title: Applications to Stability of Time-Varying Linear Dynamic Systems Under Eventually Impulsive Parameterizations Destination: section.3 Item: Title: Numerical Examples Destination: section.4 Children: Item: Title: Example 1: Time-Varying Systems with Stable Dynamic Matrix and Non-Impulsive and Impulsive Behavior Destination: subsection.4.1 Item: Title: Example 2: Unstable Dynamic Matrix Destination: subsection.4.2 Item: Title: Example 3: Impulsive Switched Systems Destination: subsection.4.3 Item: Title: Conclusions Destination: section.5 Item: Title: References Destination: section.6 Info: Title: Fixed Points of Self-Mappings with Jumping Effects: Application to Stability of a Class of Impulsive Dynamic Systems Author: Manuel De la Sen, Asier Ibeas, Aitor J. Garrido and Izaskun Garrido Subject: This paper studies the boundedness and convergence properties of the sequences generated by strict and weak contractions in metric spaces, as well as their fixed points, in the event that finite jumps can take place from the left to the right limits of the successive values of the generated sequences. An application is devoted to the stabilization and the asymptotic stabilization of impulsive linear time-varying dynamic systems of the n-th order. The impulses are formalized based on the theory of Dirac distributions. Several results are stated and proved, namely, (a) for the case when the time derivative of the differential system is impulsive at isolated time instants; (b) for the case when the matrix function of dynamics is almost everywhere differentiable with impulsive effects at isolated time instants; and (c) for the case of combinations of the two above effects, which can either jointly take place at the same time instants or at distinct time instants. In the first case, finite discontinuities of the first order in the solution are generated; that is, equivalently, finite jumps take place between the corresponding left and right limits of the solution at the impulsive time instants. The second case generates, equivalently, finite jumps in the first derivative of the solution with respect to time from their left to their right limits at the corresponding impulsive time instants. Finally, the third case exhibits both of the above effects in a combined way. 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