Linear port-Hamiltonian descriptor systems

被引：0
作者：
Christopher Beattie
Volker Mehrmann
Hongguo Xu
Hans Zwart
机构：
[1] Virginia Tech,Department of Mathematics
[2] TU Berlin,Institut für Mathematik MA 4
[3] University of Kansas,5
[4] University of Twente,Department of Mathematics
来源：
Mathematics of Control, Signals, and Systems | 2018年 / 30卷
关键词：
Port-Hamiltonian system; Descriptor system; Differential-algebraic equation; Passivity; Stability; System transformation; Differentiation index; Strangeness-index; Skew-adjoint operator; 93A30; 65L80; 93B17; 93B11;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The modeling framework of port-Hamiltonian systems is systematically extended to linear constrained dynamical systems (descriptor systems, differential-algebraic equations) of arbitrary index and with time-varying constraints. A new algebraically and geometrically defined system structure is derived. It is shown that this structure is invariant under equivalence transformations, and that it is adequate also for the modeling of high-index descriptor systems. The regularization procedure for descriptor systems to make them suitable for simulation and control is modified to preserve the port-Hamiltonian form. The relevance of the new structure is demonstrated with several examples.
引用
收藏
相关论文
共 59 条
[1]  
Bunse-Gerstner A(1999)Feedback design for regularizing descriptor systems Linear Algebra Appl 299 119-151
[2]  
Byers R(1997)Regularization of linear descriptor systems with variable coefficients SIAM J Control Optim 35 117-133
[3]  
Mehrmann V(1991)Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems IEEE Trans Autom Control 36 1228-1240
[4]  
Nichols NK(1987)A general form for solvable linear time varying singular systems of differential equations SIAM J Math Anal 18 1101-1115
[5]  
Byers R(1995)Linearization of DAEs along trajectories Z Angew Math Phys 46 70-84
[6]  
Kunkel P(2008)Bond graph for dynamic modelling in chemical engineering Chem Eng Process 47 1994-2003
[7]  
Mehrmann V(1950)Generalized Hamiltonian dynamics Can J Math 2 129-148
[8]  
Byrnes CI(2018)Damped wave systems on networks: exponential stability and uniform approximations Numer Math 138 839-867
[9]  
Isidori A(2018)On structure preserving model reduction for damped wave propagation in transport networks SIAM J Sci Comput 40 A331-A365
[10]  
Willems JC(2001)Canonical transformation and stabilization of generalized Hamiltonian systems Syst Control Lett 42 217-227
123456