Design of Filters of Networked Systems via Multiple Channels Subject to Imperfect-Markov-Switching

The paper is concerned with the H∞ filtering problems for a family of discrete-time systems. The measurement signals of the system are transmitted via a network, in which multiple communication channels coexist. It is considered that only one of these channels is active for the data communication at one time instant, and the switching of activated channel is governed by a Markov chain. In each channel, the practical phenomenon of packet dropouts is taken into account, and the packet dropout rates of different channels are different. With the construction of a Lyapunov function that depends on the index of the activated channel, stochastic stability and H∞ performance criteria are established, based on which a set of H∞ filters depending on the index of the activated channel are designed. In order to show the effectiveness of the designed H∞ filter, we apply the developed theoretical results to a numerical example.