Robust estimation for discrete time‐delay Markov jump systems with sensor non‐linearity and missing measurements

Abstract

This study addresses the H ∞ filtering design issue for a class of time-delay Markov jump system with nonlinear characteristics. A stochastic system with sensor saturation and intermittent measurements is considered in the authors study. Random noise depending on state and external-disturbance are also taken into account. A decomposition approach and a bernoulli process are utilised to model the characteristic of sensor saturation and missing measurements, respectively. By transforming the filtering error system into an input-output form, sufficient conditions for the stochastic stability of the system with a prescribed H ∞ level are presented with the help of Scaled Small Gain theorem developed for stochastic systems. Based on the proposed conditions, the rubost filter design approach is proposed. A numerical example is finally provided to demonstrate effectiveness of the proposed approahc. NomenclatureThroughout this paper, R n represents the n-dimensional Euclidean space, R n×m is the set of all n × m real matrices, the superscripts '−1' and 'T', respectively, stand for the matrix inverse and matrix transpose. Sym{A} is the shorten notation for A + A T , and the notation P > 0 (respectively, P ≥ 0), for P ∈ R n×n means that P is real symmetric and positive definite (respectively, semidefinite). The symmetric elements of the symmetric matrix is represented by an asterisk ( * ), and the block-diagonal matrices are denoted by diag{. . .}. G 1 • G 2 means the series connection of mapping G 1 and G 2 . E{·} denotes the expectation operator with respect to probability measure, and for vector x(k), x E2 = E{ ∞ n=0 x(n) 2 } 1 2 .

RobustH∞Filtering for Discrete-Time Markov Jump Linear System with Missing Measurements

“…Definition 2 (see [7]). Given a scalar > 0, system (8)- (9) satisfies an ∞ noise attenuation performance index under the robustly stochastic stability condition, if it is robustly stochastically stable and, under zero initial condition, for all nonzero ∈ 2 [0 +∞) the following inequality holds:…”

“…Consider the DMJLS (1). Given a constant > 0 as the ∞ performance index, the filtering error system (8)- (9) is robustly stochastically stable and satisfies the ∞ robustness performance, if there exists a matrix > 0 satisfying the following LMIs:…”

“…On the other hand, besides the parametric uncertainties, in practical applications, the measured outputs are also usually subject to the uncertainties of randomly occurring missing phenomenon due to kinds of reasons, such as the sensor fault, external disturbance, or network data transmission loss [8,9], where only noise is regarded as the 2 Mathematical Problems in Engineering original measurements to motivate the estimator, without the prior knowledge of whether the true signals are contained or not. As to the problem of state estimation with missing measurements, a Bernoulli distribution is usually adopted to describe the missing behavior, which is considered to be firstly proposed in [10], wherein an optimal recursive filter is presented for systems with missing measurements.…”

Fault Detection for Discrete Systems With Network-Induced Nonlinearities

“…Because the fault detection filter gains A F (h), B F (h), and C F (h) are the decision matrices rather than given constant ones, it leads to that condition (22) are not LMI conditions and cannot be solved by convex optimization algorithm, we shall focus on transforming conditions in Theorem 1 into LMI form, and establishing the fault detection filter design approach in this part.…”

“…Consequently, many researchers have focused on NCSs. The filtering problem subject to network-induced communication delays was presented in [1] and [24], filtering problem subject to missing measurements was solved in [2] and [22], robust filtering problem for nonlinear stochastic systems was studied in [11] and [17], and filtering problem for nonlinear time-delay system was discussed in [18].…”