ℋ_∞ filtering and smoothing for linear discrete time-varying descriptor systems with unknown inputs

Author(s): H. Zhao ; C. Zhang ; G. Xing
DOI: 10.1049/iet-cta.2010.0565

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Author(s): H. Zhao ¹ ; C. Zhang ¹ ; G. Xing ¹
- Affiliations: 1: School of Control Science and Engineering, Shandong University, Jinan, People’s Republic of China
Source: Volume 6, Issue 5, 15 March 2012, p. 734 – 743
DOI: 10.1049/iet-cta.2010.0565 , Print ISSN 1751-8644, Online ISSN 1751-8652

This study is concerned with the finite horizon ℋ_∞ filtering and smoothing problems for linear discrete time-varying descriptor (LDTVD) systems with unknown inputs (UI). Under the condition of Y-observability, the LDTVD system is transformed into a non-descriptor system. The design of ℋ_∞ filter and smoother is equivalent to a positivity problem of a certain indefinite quadratic form. By relating this quadratic form to a Krein space state-space model, the Kalman filter theory and the innovation analysis technology are adopted to solve the formulated ℋ_∞ estimation problem. A necessary and sufficient condition for solvability of the estimation problem is proposed, and the simultaneous state and UI estimator is obtained in terms of algebraic Riccati equations. Numerical examples are provided to illustrate the performance of the ℋ_∞ filter and smoother.

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ℋ∞ filtering and smoothing for linear discrete time-varying descriptor systems with unknown inputs

ℋ∞ filtering and smoothing for linear discrete time-varying descriptor systems with unknown inputs

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ℋ_∞ filtering and smoothing for linear discrete time-varying descriptor systems with unknown inputs

ℋ_∞ filtering and smoothing for linear discrete time-varying descriptor systems with unknown inputs