Necessary and Sufficient Conditions for Componentwise Stability of Interval Matrix Systems

Păstrăvanu, Octavian; Voicu, Mihail

doi:10.1109/tac.2004.829639

Cited by 27 publications

(9 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This line of research is due to the work of [PV04]. Let us first introduce the following definition.…”

Section: Diagonal Dominance and Diagonal Invariancementioning

confidence: 99%

“…The properties of norms, therefore including the polyhedral ones, as candidate Lyapunov functions for linear system have been analyzed in [KAS92] and [Szn93]. The proposed theory of invariance of polyhedral sets is related to the theory of componentwise stability (see [Voi84,PV04,PV06] for details). Polyhedral invariant sets will be reconsidered in several context later, where further references will be provided.…”

Section: Other Classes Of Invariant Sets and Historical Notesmentioning

confidence: 99%

See 1 more Smart Citation

Set-Theoretic Methods in Control

Blanchini

Miani

2015

Systems &Amp; Control: Foundations &Amp; Applications

209

View full text Add to dashboard Cite

“…This line of research is due to the work of [PV04]. Let us first introduce the following definition.…”

Section: Diagonal Dominance and Diagonal Invariancementioning

confidence: 99%

Section: Other Classes Of Invariant Sets and Historical Notesmentioning

confidence: 99%

Set-Theoretic Methods in Control

Blanchini

Miani

2015

Systems &Amp; Control: Foundations &Amp; Applications

209

View full text Add to dashboard Cite

“…are Schur stable) [20], [21]. This assumption is not conservative because in many applications the matrix A k is given by a closed-loop matrixÃ k +B k K, whereÃ k ,B k are the open-loop matrices withÃ k , resp.B k belonging to the interval matrices [Ã], resp.…”

Section: Problem Formulationmentioning

confidence: 99%

Zonotopic set-membership estimation for interval dynamic systems

Álamo

Camacho

et al. 2012

2012 American Control Conference (ACC)

View full text Add to dashboard Cite

This paper presents an improved method for guaranteed state estimation of discrete-time linear-time varying systems affected by disturbances, noises and structured uncertainties modeled as interval uncertainties. Under the hypothesis that the disturbances and the noises are bounded, a zonotopic outer approximation of the state estimation domain is computed offering good performance and low complexity compared to the existing methods. The size of this zonotope is decreased by solving an off-line optimization problem. The advantages of the proposed approach are illustrated via a numerical example.

show abstract

“…There are many existing research efforts and applications under the term "interval" such as interval algebra [1], [2], Schur stability of interval matrices [3], [4], Hurwitz stability of interval matrices [5], [6], [7], interval polynomial matrices [8], eigenvalues of interval matrices [9], [10], [11], and robust control with parameter uncertainty [12], [13], interval polynomial [14], [15]. By using an effective method for checking the linear independency of interval vector, the robust controllability and un-controllability problems of uncertain interval systems were firstly solved in [16].…”

Section: Introductionmentioning

confidence: 99%

Robust controllability of interval fractional order linear time invariant stochastic systems

Zeng

Chen

Yang

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

We deal with the robust controllability problem of the fractional order linear time invariant (FO-LTI) stochastic systems with interval coefficients. We present a necessary and sufficient condition for the controllability problem for the case when there is no interval uncertainty. Based on the concept of linear independency of interval vectors, we formulate the approach to check the robust controllability of interval FO-LTI stochastic systems by employing some simple but very effective sufficient condition for checking the linear independency of interval vectors. Finally, an illustrative example is presented. We show that this interval FO-LTI stochastic system is weakly controllable, while the corresponding deterministic system without noise perturbation is uncontrollable.

show abstract

Necessary and Sufficient Conditions for Componentwise Stability of Interval Matrix Systems

Cited by 27 publications

References 8 publications

Set-Theoretic Methods in Control

Set-Theoretic Methods in Control

Zonotopic set-membership estimation for interval dynamic systems

Robust controllability of interval fractional order linear time invariant stochastic systems

Contact Info

Product

Resources

About