On state feedback and pole assignment of the second order coupled singular distributed parameter systems in Hilbert space

State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are changed. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the pole assignment and stabilization of the singular distributed parameter systems.

[1]  De-Xing Feng,et al.  Pole Assignment of Distributed Parameter Systems , 1990 .

[2]  Zhaoqiang Ge,et al.  Exact controllability for singular distributed parameter system in Hilbert space , 2009, Science in China Series F: Information Sciences.

[3]  K Wang ON THE POLE ASSIGNMENT FOR THE DISTRIBUTED PARAMETER SYSTEM COUPLED WITH LUMPED PARAMETER SYSTEM , 1982 .

[4]  Ge Zhao Spectrum Distribution of the Second Order Generalized Distributed Parameter Systems , 2003 .

[5]  Ge Zhaoqiang,et al.  Pole assignment of the coupled generalized system. , 2000 .

[6]  Ran Ran,et al.  Pole assignment of the first order generalized distributed parameter control systems with multi-observers , 2009, 2009 Chinese Control and Decision Conference.

[7]  P. K. C. Wang,et al.  On the Feedback Control of Distributed Parameter Systems , 1966 .

[8]  Sun Shun-Hua,et al.  On Spectrum Distribution of Completely Controllable Linear Systems , 1981 .

[9]  刘永清,et al.  VARIABLE STRUCTURE CONTROL METHOD OF STRUCTURAL STABILITY FOR SINGULAR DISTRIBUTED PARAMETER SYSTEM , 1999 .

[10]  Lucas Jódar,et al.  An implicit difference method for the numerical solution of coupled systems of partial differential equations , 1991 .

[11]  Wieslaw Marszalek,et al.  Singular distributed parameter systems , 1993 .

[12]  P. Halmos A Hilbert Space Problem Book , 1967 .

[13]  Zhu Guang-tian,et al.  Spectrum distribution of the sedond order generalized distributed parameter systems , 2003 .

[14]  Michael Renardy,et al.  On the linear stability of hyperbolic PDEs and viscoelastic flows , 1994 .

[15]  Cheng-Zhong Xu,et al.  On spectrum and Riesz basis assignment of infinite dimensional linear systems by bounded linear feedbacks , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[16]  Zhaoqiang Ge Pole assignment by feedback control of the second order coupled singular distributed parameter systems 1 , 2004 .

[17]  Zhu Guang-tian,et al.  Pole Assignment for the First Order Coupled Generalized Control System , 2000 .

[18]  Lop Fat Ho Spectral assignability of systems with scalar control and application to a degenerate hyperbolic system , 1986 .

[19]  Zhaoqiang,et al.  DEGENERATE SEMI-GROUP METHODS FOR THE EXPONENTIAL STABILITY OF THE FIRST ORDER SINGULAR DISTRIBUTED PARAMETER SYSTEMS , 2008 .

[20]  Zhaoqiang Ge,et al.  Hopf bifurcation and chaos of financial system on condition of specific combination of parameters* , 2008, J. Syst. Sci. Complex..