Dynamic Phasor Analysis of Periodic Systems

被引：25

作者：

Almer, Stefan ^{[1
]}

Jonsson, Ulf ^{[2
]}

机构：

[1] ETH, Automat Control Lab, CH-8092 Zurich, Switzerland

[2] Royal Inst Technol, Div Optimizat & Syst Theory, Dept Math, S-10044 Stockholm, Sweden

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2009年 / 54卷 / 08期

基金：

瑞典研究理事会;

关键词：

Dynamic phasor model; harmonic Lyapunov functions; linear time-periodic systems; stability analysis;

D O I：

10.1109/TAC.2009.2023970

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The paper considers stability analysis of linear time-periodic (LTP) systems based on the dynamic phasor model (DPM). The DPM exploits the periodicity of the system by expanding the system state in a Fourier series over a moving time window. This results in an L(2)-equivalent representation in terms of an infinite-dimensional LTI system which describes the evolution of time varying Fourier coefficients. To prove stability, we consider quadratic time-periodic Lyapunov candidates. Using the DPM, the corresponding time-periodic Lyapunov inequality can be stated as a finite dimensional inequality and the Lyapunov function can be found by solving a linear matrix inequality.

引用

页码：2007 / 2012

页数：6

共 12 条

[1]

ALMER S., 2008, THESIS ROYAL I TECHN

[2]

[Anonymous], 1993, Real and Functional Analysis

[3] Multifrequency averaging of DC/DC converters [J].

Caliskan, VA ;

Verghese, GC ;

Stankovic, AM .

IEEE TRANSACTIONS ON POWER ELECTRONICS, 1999, 14 (01) :124-133

[4]

Champeney D. C., 1987, A handbook of Fourier Theorems

[5]

Khalil H. K., 2002, Nonlinear Systems, V3rd

[6] PRINCIPLE OF VIBRATIONAL CONTROL - THEORY AND APPLICATIONS [J].

MEERKOV, SM .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1980, 25 (04) :755-762

[7] On the Kalman-Yakubovich-Popov lemma [J].

Rantzer, A .

SYSTEMS & CONTROL LETTERS, 1996, 28 (01) :7-10

[8] Frequency-domain analysis of linear time-periodic systems [J].

Sandberg, H ;

Möllerstedt, E ;

Bernhardsson, B .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (12) :1971-1983

[9] On approximate phasor models in dissipative bilinear systems [J].

Tadmor, G .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2002, 49 (08) :1167-1179

[10] Harmonic Lyapunov equations in continuous-time periodic systems: solutions and properties [J].

Zhou, J. .

IET CONTROL THEORY AND APPLICATIONS, 2007, 1 (04) :946-954

← 1 2 →