H∞ filtering of network-based systems with random delay

The H∞ filtering problem is studied for a class of network-based systems with random delay in discrete-time domain. A new model is proposed to describe the filtering system with random sensor-filter delay which may be longer than one sampling period. The random delay is modeled as a Markov chain and the resulting filtering error system is a Markovian switched system with random state delay. By using a properly constructed Lyapunov function and the state transform technique, sufficient conditions for the existence of the H∞ filters are presented in terms of linear matrix inequalities. An optimization problem with LMIs constraints is formulated to design the H∞ filter which guarantees that the filtering error system is mean-square exponentially stable with a prescribed decay rate and ensures an optimal H∞ disturbance attenuation level. An illustrative example is given to demonstrate the effectiveness of the proposed results.