l1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach

This paper is concerned with the l1-gain performance analysis and positive filter design for a positive discrete-time Markov jump linear system (MJLS) by using a linear programming (LP) approach. First, by constructing a linear stochastic Lyapunov function and introducing an “equivalent” determinist...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 50; no. 8; pp. 2098 - 2107
Main Authors: Zhu, Shuqian, Han, Qing-Long, Zhang, Chenghui
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 2014
Elsevier
Subjects:
[formula omitted]-gain performance
Applied sciences
Biological and medical sciences
Control
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
Linear programming
Markov jump linear systems
Markov processes
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Phytopathology. Animal pests. Plant and forest protection
Positive filter
Positive systems
Probability and statistics
Probability theory and stochastic processes
Protozoa. Invertebrates
Sciences and techniques of general use
Positive systems
Positive filter
Linear programming
Markov jump linear systems
l1-gain performance
Markov process
gain performance
Existence condition
Stability
Discrete time systems
Linear time
l
Modeling
Standards
Pest
Filter
regime switching model
Discrete time
Population dynamics
Jump process
Lyapunov function
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:This paper is concerned with the l1-gain performance analysis and positive filter design for a positive discrete-time Markov jump linear system (MJLS) by using a linear programming (LP) approach. First, by constructing a linear stochastic Lyapunov function and introducing an “equivalent” deterministic positive discrete-time linear system, necessary and sufficient conditions in the form of LP are derived for stochastic stability and l1-gain performance of the positive discrete-time MJLS. Then a sufficient condition on the existence of the desired positive l1-gain filter is provided. The desired positive l1-gain filter can be designed by solving a standard LP problem. The pest’s structured population dynamic model is employed to illustrate the effectiveness of the proposed method.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2014.05.022