Abstract
This paper considers the non-fragile distributed state estimation problem for Markov jump systems over sensor networks based on dissipative theory. Moreover, both state estimator gain variations and parameter uncertainties are assumed to be with mode-dependent for more practical modeling. On the basis of stochastic analysis and Lyapunov–Krasovskii function method, sufficient conditions with desired mode-dependent estimators are established such that the prescribed dissipative performance can be achieved. In the end, the effectiveness and applicability of the developed scheme is confirmed via the illustrative example.
Highlights
Markov jump system (MJS), as a special type of hybrid systems, has attracted increasing attention over the last few years, since it can model realistic application systems in a better way with certain abrupt phenomena in system parameters, structures or environmental disturbances
Some well-known topics of MJSs can be listed as biological systems,[1] power systems,[2] mechanical systems,[3] and so on
Many effective state estimation approaches for linear and nonlinear MJSs have been found in the literature.[4,5,6,7]
Summary
Markov jump system (MJS), as a special type of hybrid systems, has attracted increasing attention over the last few years, since it can model realistic application systems in a better way with certain abrupt phenomena in system parameters, structures or environmental disturbances. Reported works, the main contributions are stated in two aspects: (1) The MJSs model with state estimator gain perturbations and uncertainties is introduced under the dissipative theory framework for the first time. DiðtÞ = ziðtÞ À zðtÞ, the unified state estimation error system can be obtained as follows: To this end, the dissipative performance is introduced and a useful lemma is given. L k = ÀDL~k L~k : Definition 1.26 Given real symmetric matrices U , W and matrix S with appropriate dimensions, system (1) is said to be ðU , S , W Þ-dissipative in the mean-square sense if with zero initial state it holds that ðT EfhTðtÞU hðtÞgdt. The non-fragile distributed state estimation problem for MJS (1) can be solved with the given mode-dependent state estimator gains Kij, k
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