Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems
This paper aims to explore the application of sampling control technology in positive Markov jump systems (PMJSs), focusing on the exponential stability in mean and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><...
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2024-12-01
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| author | Ping Zhao Ben Niu |
| author_facet | Ping Zhao Ben Niu |
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| description | This paper aims to explore the application of sampling control technology in positive Markov jump systems (PMJSs), focusing on the exponential stability in mean and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula>-gain performance of the system. We first establish a PMJS model based on sampling control and conduct a detailed analysis of its exponential stability in mean. Subsequently, combined with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula>-gain theory, we propose a sufficient condition for PMJSs with a prescribed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula>-gain performance level, which ensures the robustness and satisfaction of performance indicators of the system in a randomly switching environment. From the sufficient conditions we have given, we can indeed see the effect of the sampling period on the system performance. Based on this sufficient condition, we further design the state feedback controller, and give the feedback gain solving algorithm based on linear programming method. A simple simulation example verifies the correctness and effectiveness of the results. The main contribution of this paper is to introduce sampling control technology into the research of PMJSs and propose a complete theoretical framework and analysis method, providing new theoretical support and practical application value for the sampling control of PMJSs. |
| format | Article |
| id | doaj-art-9902cbe8a0e2495d9bd987115149cffc |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
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| series | Mathematics |
| spelling | doaj-art-9902cbe8a0e2495d9bd987115149cffc2025-01-10T13:18:17ZengMDPI AGMathematics2227-73902024-12-0113111010.3390/math13010110Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control SystemsPing Zhao0Ben Niu1School of Information Science and Engineering, Shandong Normal University, Jinan 250358, ChinaSchool of Information Science and Engineering, Shandong Normal University, Jinan 250358, ChinaThis paper aims to explore the application of sampling control technology in positive Markov jump systems (PMJSs), focusing on the exponential stability in mean and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula>-gain performance of the system. We first establish a PMJS model based on sampling control and conduct a detailed analysis of its exponential stability in mean. Subsequently, combined with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula>-gain theory, we propose a sufficient condition for PMJSs with a prescribed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula>-gain performance level, which ensures the robustness and satisfaction of performance indicators of the system in a randomly switching environment. From the sufficient conditions we have given, we can indeed see the effect of the sampling period on the system performance. Based on this sufficient condition, we further design the state feedback controller, and give the feedback gain solving algorithm based on linear programming method. A simple simulation example verifies the correctness and effectiveness of the results. The main contribution of this paper is to introduce sampling control technology into the research of PMJSs and propose a complete theoretical framework and analysis method, providing new theoretical support and practical application value for the sampling control of PMJSs.https://www.mdpi.com/2227-7390/13/1/110positive Markov jump systemsampling controlexponential stabilityℒ1-gainrobustness |
| spellingShingle | Ping Zhao Ben Niu Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems Mathematics positive Markov jump system sampling control exponential stability ℒ1-gain robustness |
| title | Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems |
| title_full | Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems |
| title_fullStr | Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems |
| title_full_unstemmed | Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems |
| title_short | Exponential Stability and ℒ<sub>1</sub>-Gain Performance for Positive Sampled-Data Control Systems |
| title_sort | exponential stability and l sub 1 sub gain performance for positive sampled data control systems |
| topic | positive Markov jump system sampling control exponential stability ℒ1-gain robustness |
| url | https://www.mdpi.com/2227-7390/13/1/110 |
| work_keys_str_mv | AT pingzhao exponentialstabilityandlsub1subgainperformanceforpositivesampleddatacontrolsystems AT benniu exponentialstabilityandlsub1subgainperformanceforpositivesampleddatacontrolsystems |