Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays
The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. Th...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/653628 |
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| _version_ | 1832559040539918336 |
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| author | Yurong Liu Hamid Reza Karimi Xiaohui Liu |
| author_facet | Yurong Liu Hamid Reza Karimi Xiaohui Liu |
| author_sort | Yurong Liu |
| collection | DOAJ |
| description | The guaranteed cost control problem is investigated
for a class of nonlinear discrete-time systems with Markovian
jumping parameters and mixed time delays. The mixed time delays
involved consist of both the mode-dependent discrete delay and the
distributed delay with mode-dependent lower bound. The associated
cost function is of a quadratic summation form over the infinite
horizon. The nonlinear functions are assumed to satisfy
sector-bounded conditions. By introducing new Lyapunov-Krasovskii
functionals and developing some new analysis techniques,
sufficient conditions for the existence of guaranteed cost
controllers are derived with respect to the given cost function.
Moreover, a convex optimization approach is applied to search for
the optimal guaranteed cost controller by minimizing the
guaranteed cost of the closed-loop system. Numerical simulation is
further carried out to demonstrate the effectiveness of the
proposed methods. |
| format | Article |
| id | doaj-art-edea36c74aab494d9f4faebd13fb5878 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-edea36c74aab494d9f4faebd13fb58782025-02-03T01:31:01ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/653628653628Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time DelaysYurong Liu0Hamid Reza Karimi1Xiaohui Liu2Department of Mathematics, Yangzhou University, Yangzhou 225002, ChinaDepartment of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, NorwaySchool of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, ChinaThe guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. The associated cost function is of a quadratic summation form over the infinite horizon. The nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and developing some new analysis techniques, sufficient conditions for the existence of guaranteed cost controllers are derived with respect to the given cost function. Moreover, a convex optimization approach is applied to search for the optimal guaranteed cost controller by minimizing the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.http://dx.doi.org/10.1155/2013/653628 |
| spellingShingle | Yurong Liu Hamid Reza Karimi Xiaohui Liu Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays Abstract and Applied Analysis |
| title | Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays |
| title_full | Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays |
| title_fullStr | Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays |
| title_full_unstemmed | Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays |
| title_short | Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays |
| title_sort | optimal guaranteed cost control of a class of discrete time nonlinear systems with markovian switching and mode dependent mixed time delays |
| url | http://dx.doi.org/10.1155/2013/653628 |
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