Stability analysis of 2‐D discrete and continuous state‐space systems

Kanellakis, A.; Tawfik, A.; Agathoklis, P.

doi:10.1049/cth2.12224

Cited by 7 publications

(2 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The case where E is nonsingular has been quite thoroughly studied and is now rather well understood. In this case (1) is normally rewritten in the form [9, 21–23]

\begin{align} \bm{x}^{\prime }(i_1, \dots ,i_n)= & \hat{A}\bm{x}(i_1, \dots ,i_n)+\hat{B}\bm{u}(i_1, \dots ,i_n) \end{align}

\begin{align} \bm{y}(i_1, \dots ,i_n)=&C\bm{x}(i_1, \dots ,i_n\! )+D\bm{u}(i_1, \dots ,i_n) \end{align}

with

\hat{A}=E^{-1}A

, and

\hat{B}=E^{-1}B

and is said to be a regular Roesser model.…”

Section: Problem Formulation and Motivationmentioning

confidence: 99%

See 1 more Smart Citation

Admissible transformation approach to Roesser state‐space model realization of singular multidimensional systems

Zhao

Huo

et al. 2023

IET Control Theory & Appl

View full text Add to dashboard Cite

The problem of the singular Roesser (state-space) model realization of non-causal multivariate transfer (function) matrices is investigated. Specifically, the notion of so-called admissible transformation is introduced, which allows to introduce and investigate a novel invariant matrix relationship on polynomial matrices. The singular multidimensional Roesser model (SNDRM) realization is transformed to the problem of how to reduce an initial polynomial matrix associated with the given transfer matrix into the objective polynomial matrix with a specific structure. Construction procedures are developed to obtain SNDRMs by applying admissible transformations on the initial polynomial matrix. Moreover, a separated standard form is introduced for an SNDRM so that the proposed approach can effectively treat both the left and right matrix fractional descriptions of a noncausal multivariate transfer matrix in a unified manner. Non-trivial examples are provided to illustrate the details and effectiveness of the proposed approach.

show abstract

“…The case where E is nonsingular has been quite thoroughly studied and is now rather well understood. In this case (1) is normally rewritten in the form [9, 21–23]

\begin{align} \bm{x}^{\prime }(i_1, \dots ,i_n)= & \hat{A}\bm{x}(i_1, \dots ,i_n)+\hat{B}\bm{u}(i_1, \dots ,i_n) \end{align}

\begin{align} \bm{y}(i_1, \dots ,i_n)=&C\bm{x}(i_1, \dots ,i_n\! )+D\bm{u}(i_1, \dots ,i_n) \end{align}

with

\hat{A}=E^{-1}A

, and

\hat{B}=E^{-1}B

and is said to be a regular Roesser model.…”

Section: Problem Formulation and Motivationmentioning

confidence: 99%

“…The case where E is nonsingular has been quite thoroughly studied and is now rather well understood. In this case (1) is normally rewritten in the form [9,[21][22][23] x…”

Section: Problem Formulationmentioning

confidence: 99%