Robust l2–l∞ filtering for discrete-time Markovian jump linear systems with multiple sensor faults, uncertain transition probabilities and time-varying delays

In this study, the authors present the research results on the robust investigate the robust l₂-l_∞ filtering for Markovian jump linear systems with multiple sensor faults, uncertain probability transition matrix and time-varying delays. The multiple sensor faults are modelled as multiple independent Bernoulli processes with constant probabilities. The uncertain probability transition matrix is modelled via the polytopic uncertainties for each row in the transition matrix. By using the augmentation method, the filtering error system with stochastic variables is derived. Since of the stochastic variables, the traditional stability condition is not qualified for the analysis of the filtering error systems. Thus, the exponentially mean-square stability and the robust l₂-l_∞ performance are adopted for the filtering error system. By choosing the Lyapunov-based method, sufficient conditions which can guarantee the exponentially mean-square stability and the robust l₂-l_∞ performance are obtained in the forms of matrix inequalities. Based on these conditions, the filter design method is proposed and the estimator parameters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example with two modes is used to show the design procedure and the effectiveness of the proposed design approach.