Stabilization of stochastic 2D Fornasini-Marchesini systems

Abstract

The paper uses the state-space model setting to consider the stabilization of stochastic nonlinear 2D Fornasini-Marchesini systems, where the properties of stability in the second moment and exponential stability in the mean square (ESMS) are defined and sufficient conditions for their existence established. In the case of ESMS a converse theorem is also established. The property of stochastic dissipativity in the second moment is introduced and a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a new method for control law design. Two practically motivated examples are given to demonstrate the application of the new results.