Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems

In this paper, unified optimization problem for the upper stability bound ε* and the H∞ performance index γ based on state feedback is considered for singularly perturbed systems. First, a sufficient condition for the existence of state feedback controller is presented in terms of linear matrix ineq...

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Main Authors: Liu, Lei, Yang, Ying, Liu, Wan-Quan
Format: Journal Article
Published: Springer Verlag 2013
Online Access:http://hdl.handle.net/20.500.11937/30653
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author Liu, Lei
Yang, Ying
Liu, Wan-Quan
author_facet Liu, Lei
Yang, Ying
Liu, Wan-Quan
author_sort Liu, Lei
building Curtin Institutional Repository
collection Online Access
description In this paper, unified optimization problem for the upper stability bound ε* and the H∞ performance index γ based on state feedback is considered for singularly perturbed systems. First, a sufficient condition for the existence of state feedback controller is presented in terms of linear matrix inequalities such that the resulting closed-loop system is asymptotically stable if 0<ε<ε* and also guarantees H∞ performance index. Furthermore, a new algorithm to optimize these two indices simultaneously is proposed based on Nash game theory which transfers multi-objective problem into a single objective problem as well we determine the objective weights. Then an optimal state feedback controller can be derived. Finally, some numerical examples are provided to demonstrate the effectiveness and correctness of the proposed results.
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institution Curtin University Malaysia
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publishDate 2013
publisher Springer Verlag
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spelling curtin-20.500.11937-306532017-09-13T15:09:36Z Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems Liu, Lei Yang, Ying Liu, Wan-Quan In this paper, unified optimization problem for the upper stability bound ε* and the H∞ performance index γ based on state feedback is considered for singularly perturbed systems. First, a sufficient condition for the existence of state feedback controller is presented in terms of linear matrix inequalities such that the resulting closed-loop system is asymptotically stable if 0<ε<ε* and also guarantees H∞ performance index. Furthermore, a new algorithm to optimize these two indices simultaneously is proposed based on Nash game theory which transfers multi-objective problem into a single objective problem as well we determine the objective weights. Then an optimal state feedback controller can be derived. Finally, some numerical examples are provided to demonstrate the effectiveness and correctness of the proposed results. 2013 Journal Article http://hdl.handle.net/20.500.11937/30653 10.1007/s11590-013-0686-6 Springer Verlag restricted
spellingShingle Liu, Lei
Yang, Ying
Liu, Wan-Quan
Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems
title Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems
title_full Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems
title_fullStr Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems
title_full_unstemmed Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems
title_short Unified optimization H_infinity Index and Stability Bounds for Singularly Perturbed Systems
title_sort unified optimization h_infinity index and stability bounds for singularly perturbed systems
url http://hdl.handle.net/20.500.11937/30653