Bilinear Transformation of Infinite-Dimensional State-Space Systems and Balanced Realizations of Nonrational Transfer Functions

1990 ◽  
Vol 28 (2) ◽  
pp. 438-465 ◽  
Author(s):  
Raimund Ober ◽  
Stephen Montgomery-Smith
Keyword(s):  
State Space ◽  
Transfer Functions ◽  
Space Systems ◽  
Bilinear Transformation ◽  
Infinite Dimensional ◽  
Dimensional State Space ◽  
State Space Systems

scholarly journals Controllable and Observable Polynomial Description for 2D Noncausal Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-5
Author(s):  
M. S. Boudellioua
Keyword(s):  
Image Processing ◽  
Data Processing ◽  
Seismic Data ◽  
Transfer Functions ◽  
Direct Method ◽  
Two Dimensional ◽  
Space Systems ◽  
Seismic Data Processing ◽  
Dimensional State Space ◽  
State Space Systems

Two-dimensional state-space systems arise in applications such as image processing, iterative circuits, seismic data processing, or more generally systems described by partial differential equations. In this paper, a new direct method is presented for the polynomial realization of a class of noncausal 2D transfer functions. It is shown that the resulting realization is both controllable and observable.

A new method for proving the separation principle for the infinite-dimensional LQG regulator problem

2018 ◽  
Vol 36 (3) ◽  
pp. 835-848
Author(s):  
Mahyar Mahinzaeim
Keyword(s):  
State Space ◽  
New Method ◽  
Separation Principle ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Infinite Dimensional ◽  
Regulator Problem ◽  
Dimensional State Space ◽  
Standard Linear ◽  
State Space Systems

Abstract This paper gives an alternative perspective on the standard linear quadratic Gaussian regulator problem for infinite-dimensional state-space systems. We will show that when considered on an extended Hilbert state-space, the originally stochastic control problem can be phrased as a deterministic one. In this setting we obtain a new method of proof for the well-known separation principle which does not involve probabilistic considerations.

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