Asynchronous filtering for nonhomogeneous Markov jumping systems with deception attacks

•The Markov chain of target plant is characterized by nonhomogeneous, and time- varying TPs are rendered into a polytopic structure.•To describe the asynchronous phenomenon Markov chain, the HMM is proposed.•By utilizing the matrix inequality decoupling method, the constrain-based matrices are omitted, and less conservative results are obtained. This paper deals with the problem of asynchronous filtering for nonhomogeneous Markov jumping systems with deception attacks. To describe the nonhomogeneous Markov process, the polytopic-structure-based transition probabilities (TPs) are introduced. Note that TPs are characterized by time-varying property, which cover the time independent TPs as a special case. Added by a hidden Markov model, the asynchronous phenomenon among the original plant, the quantizer and the filter is revealed. By establishing the Lyapunov functional, a sufficient condition with mean square exponentially stable is acquired. Benefit from the matrix inequality decoupling method, the asynchronous filters with less conservative are achieved. Finally, two examples are presented to show the validity of the obtained strategy.