Brief Infinite horizon backward stochastic differential equation and exponential convergence index assignment of stochastic control systems

  • Authors:

  • Yazeng Liu;Shige Peng

  • Affiliations:

  • School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, People's Republic of China;School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, People's Republic of China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2002

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Abstract

This paper studies exponential convergence index assignment of stochastic control systems from the viewpoint of backward stochastic differential equation. Like deterministic control systems, it is shown that the exact controllability of an open-loop stochastic system is equivalent to the possibility of assigning an arbitrary exponential convergence index to the solution of the closed-loop stochastic system, formed by means of suitable linear feedback of the states. As an application, a sufficient and necessary condition for the existence and uniqueness of the solution of a class of infinite horizon forward-backward stochastic differential equations is provided.