A PHASE THEORY OF MULTI-INPUT MULTI-OUTPUT LINEAR TIME-INVARIANT SYSTEMS

被引：13
作者：
Chen, Wei [1 ,2 ]
Wang, Dan [3 ]
Khong, Sei zhen [4 ]
Qiu, Li [5 ,6 ]
机构：
[1] Peking Univ, Dept Mech & Engn Sci, Beijing 100871, Peoples R China
[2] Peking Univ, State Key Lab Turbulence & Complex Syst, Beijing 100871, Peoples R China
[3] KTH Royal Inst Technol, Div Decis & Control Syst, Stockholm, Sweden
[4] Natl Sun Yat sen Univ, Dept Elect Engn, Kaohsiung, Taiwan
[5] Southern Univ Sci & Technol, Shenzhen, Peoples R China
[6] Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2024年 / 62卷 / 02期
关键词：
phase theory; MIMO phase response; Phi; infty sector; small phase theorem; SPECTRAL VARIATION; GAIN-PHASE; ROBUSTNESS; MATRIX; DESIGN;
D O I：
10.1137/22M148968X
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we define the phase response for a class of multi -input multi -output (MIMO) linear time -invariant (LTI) systems whose frequency responses are (semi -)sectorial at all frequencies. The newly defined phase subsumes the well-known notion of positive real systems and is closely related to the notion of negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time -domain interpretations of phase -bounded systems via both energy signal analysis and power signal analysis.
引用
收藏
页码：1235 / 1260
页数：26
相关论文
共 59 条
[1]  
Anderson B.D. O., 1973, Network Analysis and Synthesis
[2]   HILBERT TRANSFORM AND GAIN PHASE ERROR-BOUNDS FOR RATIONAL FUNCTIONS [J].
ANDERSON, BDO ;
GREEN, M .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (05) :528-535
[3]   Systems with counterclockwise input-output dynamics [J].
Angeli, David .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (07) :1130-1143
[4]  
Bao J, 2007, ADV IND CONTROL, P1, DOI 10.1007/978-1-84628-893-7
[5]  
Bergen A.R., 2000, POWER SYSTEMS ANAL, V2nd
[6]  
Bernstein D. S., 1992, Proceedings of the 1992 American Control Conference (IEEE Cat. No.92CH3072-6), P83
[7]  
Bhus Vinay, 2021, CPSS Transactions on Power Electronics and Applications, V6, P251, DOI [10.24295/cpsstpea.2021.00024, 10.24295/CPSSTPEA.2021.00024]
[8]  
Brogliato B., 2020, DISSIPATIVE SYSTEMS, V3rd, DOI [10.1007/978-3-030-19420-8, DOI 10.1007/978-3-030-19420-8]
[9]  
Champeney D., 1987, HDB FOURIER THEOREMS
[10]   Multivariable gain-phase and sensitivity integral relations and design tradeoffs [J].
Chen, J .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (03) :373-385
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