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Realizations of the Attasi state space model for 2D filters. (English) Zbl 0539.93013
Given a sequence of matrix Markov parameters \(W_{ij},i,j=1,2,...,N\), a matrix quadruple \(\{F_ 1,F_ 2,G,H\}\) is sought so that \(W_{ij}=HF_ 2^{j-1}\quad F_ 1^{i-1}G. \{F_ 1,F_ 2,G,H\}\) are the matrices in the local state-space realization, \[ x(i+1,\quad j+1)=F_ 1x(i,j+1)+F_ 2x(i+1,j)+F_ 0x(i,j)+Gu(i,j),y(i,j)=Hx(i,j), \] with i,\(j\geq 0\), \(F_ 0=-F_ 1F_ 2\) or \(F_ 0=-F_ 2F_ 1,u(i,j)\) is the input, y(i,j) is the output and x(i,j) represents the local state vector. The requirement of commutativity, \(F_ 1F_ 2=F_ 2F_ 1\), in the original Attasi model is dispensed with here. The existece of a realization from given \(\{W_{ij}\}\) is established, conditions concerning uniqueness of the realization are given and a necessary and sufficient condition for the state-space model to be minimal is proved.
Reviewer: N.K.Bose
MSC:
93B20 Minimal systems representations
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
93B15 Realizations from input-output data
93B10 Canonical structure
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93C55 Discrete-time control/observation systems
93E11 Filtering in stochastic control theory
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References:
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