H∞ filtering for time-delayed singular Markovian jump systems with time-varying switching: A quantized method

• The underlying TRM is studied by the quantized method, whose difficulties used with infinite precision are overcome.
• New criteria depending on time delay and quantization density simultaneously are developed.
• Several sufficient conditions for the existence of the desired filter are all given in the form of LMIs.
• Even for some special cases, our results are also less conservative than some existing results.

This paper discusses the H∞H∞ filtering problem of time-delayed singular Markovian jump systems (SMJSs) with time-varying transition rate matrix (TRM). In this paper, the underlying TRM is studied by the quantized method, whose difficulties used in system analysis and synthesis with infinite precision are overcome. Based on the proposed quantization principle, the time-varying TRM is firstly quantized into a series of finite TRMs with norm bounded uncertainties. Then, new criteria depending on time delay and quantization density simultaneously are developed such that the corresponding system is stochastic admissible with an H∞H∞ performance. Several sufficient conditions for the existence of the desired filter are given in the form of linear matrix inequalities (LMIs). Finally, numerical examples are used to demonstrate the correctness and superiorities of the proposed methods.