Protocol‐based H ∞ filtering for piecewise linear systems: A measurement‐dependent equivalent reduction approach

In this article, a protocol‐based H ∞ filtering problem is investigated for piecewise linear (PWL) systems with mixed delays. Stochastic access protocol (SAP) is utilized to schedule the signal transmission via a constrained communication channel, under which only one measurement value can be transmitted to the filter at each time instant following a Markov process. When SAP is applied to PWL systems, only a part of system modes can be observed due to the incomplete measurement information. Therefore, a measurement‐dependent parameter storage rule with a certain probability distribution is introduced to overcome the difficulties coming from SAP‐induced incomplete information. By resorting to the proposed mode storage rule, a novel measurement‐dependent asynchronous H ∞ filter model is constructed and the problem is converted into a new switching process of a larger state space following a reconstructed Markov process. Subsequently, a sufficient condition is established to guarantee the H ∞ performance, and the probability‐dependent filter parameters are obtained by applying the stochastic analysis technique. Finally, a numerical example is given to show the effectiveness of the design approach.