Non-fragile filtering for singular Markovian jump systems with missing measurements

- An novel algorithm is developed for non-fragile filter design of a discrete-time singular Markovian jump system with time-varying delay and external disturbance, which can unify both mode-dependent and mode-independent filter designs in a single framework.
- In the considered discrete-time system, the missing measurement concept is taken into account in which the missing probability is assumed to be affected by the norm-bounded uncertainties.
- Based on the extended passivity theory, sufficient conditions are established that ensure the stochastic admissibility of the considered system, where the Abel Lemma based finite-sum inequality is employed for reducing the conservatism of the obtained conditions.

In this paper, the issue of an non-fragile filter design is addressed for a class of discrete-time singular Markovian jump systems subject to time-varying delay and missing measurements based on the extended passivity theory. In particular, the missing probability is assumed to be affected by norm-bounded uncertainties. Moreover, the proposed filter design is more general and realistic since it unifies the mode-independent and mode-dependent characteristics in a single framework. By using Lyapunov-Krasovskii stability theory and Abel lemma, a new set of sufficient conditions is established which ensures the stochastic admissibility of the resulting error system with a prescribed disturbance attenuation level. Based on the sufficient conditions, the explicit expression of the desired filter gain matrices is formulated in terms of linear matrix inequalities. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed non-fragile filter design, wherein it is showed that the proposed method yields less conservative results over some existing methods.