Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances

The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer e...

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Published in:	International journal of systems science Vol. 47; no. 13; pp. 3193 - 3205
Main Authors:	Nguyen, M. C., Trinh, H., Nam, P. T.
Format:	Journal Article
Language:	English
Published:	Taylor & Francis 02.10.2016
Subjects:	Algorithms Design engineering discrete-time systems Disturbances Errors Feasibility Mathematical models Observers Optimization time-varying delay unknown bounded disturbances ε-Bounded state estimation
ISSN:	0020-7721, 1464-5319
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Abstract	The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ε-convergent, which means that the estimate converges robustly within an ε-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ε-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ε. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.
AbstractList	The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ε-convergent, which means that the estimate converges robustly within an ε-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ε-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ε. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results. The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is epsilon -convergent, which means that the estimate converges robustly within an epsilon -bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for epsilon -convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for epsilon . Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.
Author	Trinh, H. Nguyen, M. C. Nam, P. T.
Author_xml	– sequence: 1 givenname: M. C. surname: Nguyen fullname: Nguyen, M. C. organization: School of Engineering, Deakin University – sequence: 2 givenname: H. surname: Trinh fullname: Trinh, H. email: hieu.trinh@deakin.edu.au organization: School of Engineering, Deakin University – sequence: 3 givenname: P. T. surname: Nam fullname: Nam, P. T. organization: Department of Mathematics, Quynhon University
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Title	Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances
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