Robust l ₂ – l _∞ filtering for discrete‐time Markovian jump linear systems with multiple sensor faults, uncertain transition probabilities and time‐varying delays

Abstract

In this study, the authors present the research results on the robust investigate the robust l 2-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 l 2-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 l 2-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.

Distributed robust filtering with hybrid consensus strategy for sensor networks

“…This assumption is not, however, guaranteed and the performance of Kalman filtering would be degraded inevitably since most practical systems have model uncertainties. Hence, to reduce the effect of non-satisfaction condition in the accuracy of estimation, robust Kalman filtering schemes are introduced, for instance, see [31][32][33][34]. In general, uncertainties in systems can be categorised into two different classes including uncertainty in parameters of the model, and uncertainty in the observation process.…”

Linear minimum‐mean‐square error estimation of Markovian jump linear systems with randomly delayed measurements

“…Compute the state estimateX a k|k by (12), and obtain its covariance W a k|k by (13) Step 6: Output. Computex k|k by accumulating all state estimates in each mode fromĵ k|k by (8), and obtain the covariance P k|k by (9) Step 7: Set k−1 ← k and go to Step 3 Fig. 2 Recursive structure of the LMMSE estimator in [9] 4 Numerical example A numerical example for the discrete-time MJLSRDM is presented in this section based on two Markovian states to compare the LMMSE estimator in [9], the interacting multiple model (IMM) method where the estimator in [21] or [23] for the one-step or two-step randomly delayed measurements case under the linear system is adopted in each mode, and the proposed LMRDE estimator.…”

“…Considerable research has been undertaken in the field of estimation theory in relation to the discrete-time Markovian jump systems, such as non-linear filtering [1][2][3][4][5], target tracking [6,7] and fault-tolerant robust filtering [8].…”

Robust reliable dissipative filtering for networked control systems with sensor failure

“…Filtering problem has wide applications in signal‐processing, communications and control application [8]. In recent years, estimating a state or a parameter through filter design has attracted considerable research interest see [9–14]. For example, a distributed fusion filtering problem for a class of networked multi‐sensor fusion systems with communication bandwidth constraints has been investigated in [15].…”