Robust disturbance-rejection problems with finite-dimensional dynamic compensator for infinite-dimensional systems

1997 ◽  
Author(s):  
N. Otsuka ◽  
H. Inaba
Keyword(s):  
Disturbance Rejection ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
Dynamic Compensator

scholarly journals Generalized -Pairs for Uncertain Linear Infinite-Dimensional Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Naohisa Otsuka ◽  
Haruo Hinata
Keyword(s):  
Disturbance Rejection ◽  
Invariant Subspaces ◽  
Solvability Conditions ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Dynamic Compensator

We introduce the concept of generalized -pairs which is related to generalized -invariant subspaces and generalized -invariant subspaces for infinite-dimensional systems. As an application the parameter-insensitive disturbance-rejection problem with dynamic compensator is formulated and its solvability conditions are presented. Further, an illustrative example is also examined.

Modeling and boundary control of infinite dimensional systems in the Brayton–Moser framework

2017 ◽  
Vol 36 (2) ◽  
pp. 485-513
Author(s):  
Krishna Chaitanya Kosaraju ◽  
Ramkrishna Pasumarthy ◽  
Dimitri Jeltsema
Keyword(s):  
Boundary Control ◽  
Zero Energy ◽  
Line System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
Boundary Control Problem ◽  
Energy Flows ◽  
Admissible Pairs ◽  
The Stability

Abstract It is well documented that shaping the energy of finite-dimensional port-Hamiltonian systems by interconnection is severely restricted due to the presence of dissipation. This phenomenon is usually referred to as the dissipation obstacle. In this paper, we show the existence of dissipation obstacle in infinite dimensional systems. Motivated by this, we present the Brayton–Moser formulation, together with its equivalent Dirac structure. Analogous to finite dimensional systems, identifying the underlying gradient structure is crucial in presenting the stability analysis. We elucidate this through an example of Maxwell’s equations with zero energy flows through the boundary. In the case of mixed-finite and infinite-dimensional systems, we find admissible pairs for all the subsystems while preserving the overall structure. We illustrate this using a transmission line system interconnected to finite dimensional systems through its boundary. This ultimately leads to a new passive map, using this we solve a boundary control problem, circumventing the dissipation obstacle.

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