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

• Linear stochastic differential systems of descriptor type.
• Matrix coefficients with structure: symmetric/skew-symmetric cases.
• Solvability for any terminal condition and exact controllability.
• Applications to controlled mechanical translations system.

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.