Conditioned invariance and unknown-input observation for two-dimensional Fornasini-Marchesini models

2009 International Workshop on Multidimensional (nD) Systems

Yang

2009

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This paper collects, in a unified way, some recent results on a geometric approach to two-dimensional (2-D) system analysis and synthesis. The concepts of controlled and conditioned invariant subspaces, stabilisability and detectability subspaces, and output-nulling and input-containing subspaces, which prove useful in solving various 2-D filtering and decoupling problems, are developed for the Fornasini-Marchesini model in a general form.

Section: B Internal and External Stability Ofinvariant Subspacesmentioning

confidence: 98%

“…• Conditioned invariance is linked to the existence of 2-D quotient observers [15]. For an observer of the fomr'…”

Section: Definition 4: the Subspace Y~jrn Is Conditioned Invariant Fomentioning

confidence: 99%

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Controlled and conditioned invariance with stability for two-dimensional systems

2009 International Workshop on Multidimensional (nD) Systems

Yang

2009

Self Cite

“…. 23Detectability input-containing subspaces can be linked to the existence of certain observers [28].…”

Section: Detectability Subspaces and Local State Observersmentioning

confidence: 99%

Detectability subspaces and observer synthesis for two-dimensional systems

Multidim Syst Sign Process

2010

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The notions of input-containing and detectability subspaces are developed within the context of observer synthesis for two-dimensional (2-D) Fornasini-Marchesini models. Specifically, the paper considers observers which asymptotically estimate the local state, in the sense that the error tends to zero as the reconstructed local state evolves away from possibly mismatched boundary values, modulo a detectability subspace. Ultimately, the synthesis of such observers in the absence of explicit input information is addressed.

“…Conditioned invariance is linked to the exisitence of 2-D quotient observers [22]. For an observer of the form (2) for (1) with u i, j = 0, 4 it follows that with e i, j :=…”

Section: Conditioned Invariant Subspacesmentioning

confidence: 99%

Asymptotic quotient observers for 2-D Fornasini Marchesini models

2009 17th Mediterranean Conference on Control and Automation

2009

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The concepts of conditioned-invariant, detectability and input-containing subspaces are developed within the context of observer design for 2-D Fornasini-Marchesini models in a general form. Specifically, a link is establised between these subspaces and the existence of so-called quotient observers, which estimate the local state modulo a conditioned invariant subspace. We also consider the synthesis of observers that are asymptotic in the sense that the estimation error (modulo a conditioned invariant subspace) tends to zero away from the boundary values. x i+1, j+1 = A 0 x i, j + A 1 x i+1, j + A 2 x i, j+1 +B 0 u i, j + B 1 u i+1, j + B 2 u i, j+1 , y i, j = Cx i, j + Du i, j , (1) of Kurek [18]. Our approach to defining conditioned invariant subspaces is similar to that of Willems in that we ultimately seek an observer of the form 1 ω i+1, j+1 = K 0 ω i, j + K 1 ω i+1, j + K 2 ω i, j+1 +L 0 y i, j + L 1 y i+1, j + L 2 y i, j+1 , (2) so that the estimation error e i, j Qx i, j − ω i, j , for some full row-rank matrix Q, 2 asymptotically approaches zero away from standard boundary conditions. To this end, we develop notions of conditioned-invariant, detectability and This work was supported in part by the Australian Research Council