Dissipative Hamiltonian Realization of Nonlinear Differential Algebraic Systems

Hamiltonian function method is important in the analysis and synthesis of nonlinear differential algebraic systems (NDAS), where the key process is to complete the dissipative Hamiltonian realization (DHR) of the considered system,. In this paper, we discuss the DHR problem of NDAS. First, a sufficient condition is given to complete the constant DHR. The construction of constant DHR of NDAS is discussed as well. Then, for NDAS which does not possess a desired DHR, the feedback controller is designed to re-assign the structure of DHR. The asymptotical stability of the closed loop system is also analized.

[1]  Pravin Varaiya,et al.  A structure preserving energy function for power system transient stability analysis , 1985 .

[2]  Hariharan Krishnan,et al.  Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems , 1994, Autom..

[3]  H. Schättler,et al.  Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability] , 1995, Proc. IEEE.

[4]  R. Ortega,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[5]  R. Ortega,et al.  A Passivation Approach to Power Systems Stabilization , 1998 .

[6]  Daizhan Cheng,et al.  Energy-Based Stabilization of Forced Hamiltonian Systems with its Application to Power Systems , 1999 .

[7]  François Delebecque,et al.  Nonlinear Descriptor Systems , 1999 .

[8]  R. Ortega,et al.  Adaptive L/sub 2/ disturbance attenuation of Hamiltonian systems with parametric perturbation and application to power systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[9]  Daizhan Cheng,et al.  Geometric structure of generalized controlled Hamiltonian systems and its application , 2000 .

[10]  Daizhan Cheng,et al.  Passivity-based stabilization and H 8 control of the Hamiltonian control systems with dissipation and its applications to power systems , 2000 .

[11]  Arjan van der Schaft,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[12]  Romeo Ortega,et al.  Putting energy back in control , 2001 .

[13]  Fan-Ren Chang,et al.  H∞ control for nonlinear descriptor systems , 2006, IEEE Trans. Autom. Control..

[14]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[15]  R. Ortega,et al.  Adaptive L2 Disturbance Attenuation Of Hamiltonian Systems With Parametric Perturbation And Application To Power Systems , 2003 .

[16]  Yanhong Liu,et al.  Feedback control of nonlinear differential algebraic systems using Hamiltonian function method , 2006, Science in China Series F: Information Sciences.