H∞ Filtering for 2D Discrete Switched Stochastic Systems: An Extended Average Dwell Time Approach, Part I

This paper deals with the problem of H
_∞
filtering for 2D discrete switched stochastic systems described by the Fornasini-Marchesini model. Our purpose is to design a filter such that the filtering error system is guaranteed to be mean square asymptotically with a prescribed H
_∞
disturbance attenuation level by using the switched quadratic Lyapunov function and the piecewise Lyapunov function approach under the arbitrary switched signals. Moreover, the notion of time instant for 2D switched systems is introduced. To highlight the effectiveness of the proposed filter design, a numerical example is given.