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...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer Verlag
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/30653 |
| _version_ | 1848753149223895040 |
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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. |
| first_indexed | 2025-11-14T08:19:55Z |
| format | Journal Article |
| id | curtin-20.500.11937-30653 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:19:55Z |
| publishDate | 2013 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |