On the Lipschitz Behavior of Solution Maps of a Class of Differential Inclusions

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• 作者：Luká? Adam
• 关键词：Differential inclusions ; Lipschitzian continuity ; Stability ; Variational analysis ; Electrical circuits ; 34A60 ; 34H05 ; 49K21 ; 34A36
• 刊名：Set-Valued and Variational Analysis
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：23
• 期：3
• 页码：559-575
• 全文大小：351 KB
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• 作者单位：Luká? Adam (1)
  
  1. Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou vě?í 4, 182 08, Prague 8, Czech Republic
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

We consider a general differential inclusion which is parameterized by a parameter. We perform time discretization and present conditions under which the discretized solution map is locally Lipschitz. Further, if the Lipschitzian modulus is bounded in some sense, we show that it is possible to obtain the local Lipschitzian property even for the original (not discretized) solution map. We conclude the paper with an example concerning stability analysis of nonregular electrical circuits with ideal diodes.