Advances on the Reachability Index of Positive 2-D Systems

Bailo, Esteban; Gelonch, Josep; Romero‐Vivó, Sergio

doi:10.1109/tac.2014.2303218

Cited by 8 publications

(16 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, and the last inequality is from (9). It should point that (12) holds irrespective of whether k + l − h (k) and k + l − v (l) are nonnegative or not.…”

Section: Assumptionmentioning

confidence: 99%

“…Due to their structures and applications, the Roesser model and the Fornasini‐Marchesini model are the most frequently used to describe 2D systems and have attracted considerable attention in the past few decades . In particular, some results on the dynamical properties of 2D positive systems have been reported . Positive dynamical systems are those systems, whose state variables are nonnegative whenever the initial conditions are nonnegative.…”

Section: Introductionmentioning

confidence: 99%

“…[6][7][8] In particular, some results on the dynamical properties of 2D positive systems have been reported. [9][10][11] Positive dynamical systems are those systems, whose state variables are nonnegative whenever the initial conditions are nonnegative. Chu and Liu 12 studied the asymptotic stability of 2D positive systems represented by a model of Roesser type.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

Tian

Liu

Wang

2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary In this paper, we aim to investigate the stability of 2D switched positive nonlinear systems with time‐varying delays in the Roesser model, which includes 2D switched positive linear systems as a special case. By using the average dwell time approach, we give a sufficient condition for the exponential stability of 2D switched positive nonlinear systems. The difficulty caused by the delays is overcome by introducing a model transform and the method used in this paper is different from conventional Lyapunov‐Krasovskii functional method. An explicit exponential bound on the decay rate is presented. We also extend the result to the general 2D switched linear systems, not necessarily positive. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

show abstract

“…, and the last inequality is from (9). It should point that (12) holds irrespective of whether k + l − h (k) and k + l − v (l) are nonnegative or not.…”

Section: Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

Tian

Liu

Wang

2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…This index plays an important role because it enables us to determine in a finite number of steps whether a system is locally reachable or not as well as to know how many separations sets at most are needed to achieve the states. Previous studies such as [10], [11], [16] and references therein, [20] and [21] have studied and reported that the reachability index for positive 1-D systems is always bounded by the dimension n. However, several attempts in two dimensional case (see [1], [2] and [9] and references therein) have been made to obtain a general formula depending on n on the local reachability index for any positive 2-D systems. So far, despite the use of graph-theoretic techniques, to solve this question seems to be a nontrivial goal to accomplish due to its computational complexity (see [30]).…”

Section: Introductionmentioning

confidence: 99%

A first cubic upper bound on the local reachability index for some positive 2-D systems

Bailo

Gelonch

Romero‐Vivó

2019

RACSAM

Self Cite

View full text Add to dashboard Cite

The calculation of the smallest number of steps needed to deterministically reach all local states of an nth-order positive 2-D system, which is called local reachability index (I LR ) of that system, was recently tackled by means of the use of a suitable composition table. The greatest index I LR obtained in the previous literature was n + 3 (⌊n/2⌋) 2 for some appropriated values of n. Taking as a basis both a combinatorial approach of such systems and the construction of suitable geometric sets in the plane, an upper bound on I LR depending on the dimension n for a new family of systems is characterized. The 2-D influence digraph of this family of order n ≥ 6 consists of two subdigraphs corresponding to a unique source s. The first one is a cycle involving the first n 1 vertices and is connected to the another subdigraph through the 1-arc (2, n 1 + n 2 ), being the natural numbers n 1 and n 2 such that n 1 > n 2 ≥ 2 and n − n 1 − n 2 ≥ 1. The second one has two main cycles, a cycle where only the remaining vertices n 1 + 1, . . . , n appear and a cycle containing only the vertices n 1 + 1, . . . , n 1 + n 2 − 1. Moreover, the last vertices are connected through the 2-arc (n 1 + n 2 − 1, n). Furthermore, if n ≥ 12 and is a multiple of 3, for appropriate n 1 and n 2 , the I LR of that family is at least

show abstract

“…In addition, 2D discrete system also has wide applications in digital filter, image enhancement, image sharpening, signal processing and other fields [2]. Wide application background makes the stability analysis, control synthesis and filtering design of 2D discrete system has become the research focus of many scholars at home and abroad [3–10].…”

Section: Introductionmentioning

confidence: 99%

Improved approach to delay‐dependent stability and stabilisation of two‐dimensional discrete‐time systems with interval time‐varying delays

Peng

Chen

2015

IET Control Theory & Applications

View full text Add to dashboard Cite

Advances on the Reachability Index of Positive 2-D Systems

Cited by 8 publications

References 23 publications

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

A first cubic upper bound on the local reachability index for some positive 2-D systems

Improved approach to delay‐dependent stability and stabilisation of two‐dimensional discrete‐time systems with interval time‐varying delays

Contact Info

Product

Resources

About