Linear backward stochastic differential systems of descriptor type with structure and applications to engineering

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Abstract

In this paper, a class of linear stochastic differential systems of descriptor type with symmetric and skew-symmetric coefficients is considered. These kinds of systems have numerous applications in several areas of engineering, systems and control theory with potential applications to multibody systems (constrained mechanical systems with singular mass matrices), power systems, robotics and elsewhere. Thus, in our approach, using the Thompson canonical form for regular pencils, necessary and sufficient conditions for the solvability of a general class of such systems are obtained. In addition, as interesting theoretical applications, the solvability for any terminal condition and the problem of exact controllability are completely settled. An application to controlled mechanical translation systems illustrates the main findings of the paper.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalProbabilistic Engineering Mechanics
Volume40
DOIs
Publication statusPublished - Apr 2015
Externally publishedYes

Keywords

  • Constraint systems
  • Exact controllability
  • Linear stochastic descriptor equations
  • Singular mass matrices
  • Solvability

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