Reliable H∞ filtering for discrete time-delay Markovian jump systems with partly unknown transition probabilities

Abstract

In this paper, the reliable H ∞ filtering problem is studied for a class of discrete nonlinear Markovian jump systems with sensor failures and time delays. The transition probabilities of the jumping process are assumed to be partly unknown. The failures of sensors are quantified by a variable taking values in a given interval. The time-varying delay is unknown with given lower and upper bounds. The purpose of the addressed reliable H ∞ filtering problem is to design a mode-dependent filter such that the filtering error dynamics is asymptotically mean-square stable and also achieves a prescribed H ∞ performance level. By using a new Lyapunov-Krasovskii functional and delay-partitioning technique, sufficient delay-dependent conditions for the existence of such a filter are obtained. The filter gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A numerical example is provided to demonstrate the effectiveness of the proposed design approach.

New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

“…In comparison with some existing results on stability and performance analysis for MJLSs [5,7,9,19], the results given in Theorem 1 have some merits. Firstly, the MJLSs under consideration are subject to a Markov stochastic process simultaneously consisting of exactly known, uncertain, and partially unknown TPs, which are more general and practical.…”

New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

“…In comparison with some existing results on stability and performance analysis for MJLSs [5,7,9,19], the results given in Theorem 1 have some merits. Firstly, the MJLSs under consideration are subject to a Markov stochastic process simultaneously consisting of exactly known, uncertain, and partially unknown TPs, which are more general and practical.…”

and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

“…Note that because the slack variables used in Theorem 1 are polynomially dependent with degree h on the uncertain parameters, the increasing of h implies mainly in the growth of the number of variables. On the other hand, greater values of g produce a larger number of LMI rows, mostly because of conditions (13) and (14). Although the Pólya's relaxation level d does not change the number of variables, the rising of the number of LMI rows is directly related to higher values of d .…”

Quantized Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

“…and (2is)   are defined in (13). Moreover, if the above conditions have a set of feasible solutions…”

New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

“…In comparison with some existing results on stability and performance analysis for MJLSs [5,7,9,19], the results given in Theorem 1 have some merits. Firstly, the MJLSs under consideration are subject to a Markov stochastic process simultaneously consisting of exactly known, uncertain, and partially unknown TPs, which are more general and practical.…”

and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

“…Note that because the slack variables used in Theorem 1 are polynomially dependent with degree h on the uncertain parameters, the increasing of h implies mainly in the growth of the number of variables. On the other hand, greater values of g produce a larger number of LMI rows, mostly because of conditions (13) and (14). Although the Pólya's relaxation level d does not change the number of variables, the rising of the number of LMI rows is directly related to higher values of d .…”

Quantized Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

“…and (2is)   are defined in (13). Moreover, if the above conditions have a set of feasible solutions…”

New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

“…In comparison with some existing results on stability and performance analysis for MJLSs [5,7,9,19], the results given in Theorem 1 have some merits. Firstly, the MJLSs under consideration are subject to a Markov stochastic process simultaneously consisting of exactly known, uncertain, and partially unknown TPs, which are more general and practical.…”

and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

“…Note that because the slack variables used in Theorem 1 are polynomially dependent with degree h on the uncertain parameters, the increasing of h implies mainly in the growth of the number of variables. On the other hand, greater values of g produce a larger number of LMI rows, mostly because of conditions (13) and (14). Although the Pólya's relaxation level d does not change the number of variables, the rising of the number of LMI rows is directly related to higher values of d .…”

Quantized Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

“…and (2is)   are defined in (13). Moreover, if the above conditions have a set of feasible solutions…”