Stability Analysis Of 2-D Switched Systems With Multiplicative Noise And Expceted Power Bound Of 2-D Digital Filters With Multiplicative Noise

The two-dimensional(2-D)systems are hot topics both for their theoretical sig-nificance and for their practical importance in various areas,such as water steam heat-ing,biomedical engineering,electric power engineering and image enhancement.This paper introduces two new classes of discrete-time 2-D switched systems with multiplicative noise and 2-D digital filters for the Fornasini-Marchesini local state-space(FMLSS)model with multiplicative noise.In this paper,we study two problems:one is the stability analysis of the above two new systems;the other one is the 2-D expected power bound(EPB)of 2-D digital filters with multiplicative noise in the FMLSS model.Firstly,we establish a sufficient stochastic stability condition for 2-D switched systems with multiplicative noise under arbitrary switching signal.Secondly,by introducing the average dwell time into this new model and combining with the Lyapunov function,we investigate the stochastic exponentially stability of the 2-D switched systems with multiplicative noise for the restricted switching case.Next,we investigate the stability for a 2-D digital filter with multiplicative noise in the FMLSS model with/without a stabilization controller.Then,we give the definition of expected power bound(EPB)for 2-D digital filters in the FMLSS model with Wiener process noise,and establish some sufficient conditions of 2-D EPB for this new model with/without a stabilization controller.Finally,some numerical examples are provided to verify the effectiveness and feasibility of the proposed results.This paper introduced the random matrices to characterize the phenomenon of the random variations in the coefficients of the discrete-time 2-D switched model.Such a description is more suitable for reflecting coefficient variations of a random nature form roundoff errors generated by logarithmic quantizer in numerical computation,and proposed the notion of 2-D Expected power bound(EPB)for dealing with the effect of stochastic noise on 2-D digital filters with multiplicative noise.