H∞ filtering of Markov jump linear systems with general transition probabilities and output quantization

- Transition probabilities are known, uncertain with variations and unknown.
- New measurements are developed to deal with the nonlinearities induced by quantization and unknown transition probabilities.
- A flexible filter design method is established in terms of LMIs.

This paper addresses the H∞ filtering of continuous Markov jump linear systems with general transition probabilities and output quantization. S-procedure is employed to handle the adverse influence of the quantization and a new approach is developed to conquer the nonlinearity induced by uncertain and unknown transition probabilities. Then, sufficient conditions are presented to ensure the filtering error system to be stochastically stable with the prescribed performance requirement. Without specified structure imposed on introduced slack variables, a flexible filter design method is established in terms of linear matrix inequalities. The effectiveness of the proposed method is validated by a numerical example.