{"title":"Coefficient-based conditions of matrix-valued real-rational proper negative imaginary functions","authors":"Qian Zhang, Liu Liu, Yufeng Lu","doi":"10.1002/asjc.3521","DOIUrl":null,"url":null,"abstract":"<p>This paper mainly gives sufficient coefficient-based conditions of matrix-valued real-rational proper negative imaginary (NI) functions. The proper NI functions can be divided into three cases by relative order, namely, NI functions with relative order 0, 1, and 2. Based on the relationship between NI functions with poles at 0 and without poles at 0, as well as coefficient-based conditions of positive real functions, sufficient coefficient-based conditions are shown of NI functions with relative order 1 and 2. These main results are related to the numerical radius and Crawford number of matrices. Moreover, they are supplements to some existing results. NI functions with relative order 0 can be changed into the case of relative order 1, and the sufficient coefficient-based conditions are also obtained of NI functions with relative order 0. In addition, the coefficient-based conditions can be used to construct interval NI functions, and some examples are given to illustrate the main results.</p>","PeriodicalId":55453,"journal":{"name":"Asian Journal of Control","volume":"27 3","pages":"1594-1601"},"PeriodicalIF":2.7000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Control","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asjc.3521","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper mainly gives sufficient coefficient-based conditions of matrix-valued real-rational proper negative imaginary (NI) functions. The proper NI functions can be divided into three cases by relative order, namely, NI functions with relative order 0, 1, and 2. Based on the relationship between NI functions with poles at 0 and without poles at 0, as well as coefficient-based conditions of positive real functions, sufficient coefficient-based conditions are shown of NI functions with relative order 1 and 2. These main results are related to the numerical radius and Crawford number of matrices. Moreover, they are supplements to some existing results. NI functions with relative order 0 can be changed into the case of relative order 1, and the sufficient coefficient-based conditions are also obtained of NI functions with relative order 0. In addition, the coefficient-based conditions can be used to construct interval NI functions, and some examples are given to illustrate the main results.
期刊介绍：
The Asian Journal of Control, an Asian Control Association (ACA) and Chinese Automatic Control Society (CACS) affiliated journal, is the first international journal originating from the Asia Pacific region. The Asian Journal of Control publishes papers on original theoretical and practical research and developments in the areas of control, involving all facets of control theory and its application.
Published six times a year, the Journal aims to be a key platform for control communities throughout the world.
The Journal provides a forum where control researchers and practitioners can exchange knowledge and experiences on the latest advances in the control areas, and plays an educational role for students and experienced researchers in other disciplines interested in this continually growing field. The scope of the journal is extensive.
Topics include:
The theory and design of control systems and components, encompassing:
Robust and distributed control using geometric, optimal, stochastic and nonlinear methods
Game theory and state estimation
Adaptive control, including neural networks, learning, parameter estimation
and system fault detection
Artificial intelligence, fuzzy and expert systems
Hierarchical and man-machine systems
All parts of systems engineering which consider the reliability of components and systems
Emerging application areas, such as:
Robotics
Mechatronics
Computers for computer-aided design, manufacturing, and control of
various industrial processes
Space vehicles and aircraft, ships, and traffic
Biomedical systems
National economies
Power systems
Agriculture
Natural resources.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
