T–S fuzzy-model-based H2H2 and H∞H∞ filtering for networked control systems with two-channel Markovian random delays

This paper is concerned with the two-mode-dependent filtering problem in networked control systems (NCSs) where the random external input-to-filter delay and the output-to-filter delay are modeled as Markov chains. The nonlinear discrete-time system is modeled by the Takagi–Sugeno fuzzy model. The overall filtering error system is formulated as a special jump linear system. Then definitions of H2H2 and H∞H∞ norms of the filtering error system are proposed. Moreover, the two-mode-dependent H2H2 and H∞H∞ filters are designed to incorporate the external input-to-filter delay and the output-to-filter delay using linear matrix inequality (LMI) techniques. The simulations and a numerical example illustrate the feasibility and effectiveness of the proposed method.