Two-Dimensional Peak-to-Peak Filtering for Stochastic Fornasini–Marchesini Systems

This paper is concerned with the problem of two-dimensional (2-D) stochastic peak-to-peak filter design for Fornasini-Marchesini local state-space (FM LSS) systems with state-multiplicative noise. First, a novel sufficient condition is established, which guarantees that the underlying FM LSS system is stochastically mean-square stable with 2-D stochastic peak-to-peak performance. A deterministic FM LSS system case is also discussed. Subsequently, based on the result, a new 2-D stochastic peak-to-peak filter of general form is designed for FM LSS systems with state-multiplicative noise. Finally, a numerical example is presented to show the effectiveness of the proposed 2-D stochastic peak-to-peak filter.