Solvability of 2D hybrid linear systems - comparsion of three different methods

The problems of asymptotic stability and robust stability of the new general 2D model of scalar linear dynamic continuous-discrete systems, standard and positive, are considered. Simple analytic conditions for asymptotic stability and for robust stability are given. These conditions are expressed in terms of coefficients of the model. The considerations are illustrated by numerical examples. The methods proposed can be generalized to scalar Fornasini-Marchesini and Roesser models of 2D continuous-discrete systems.

/pdf/robust-stability-of-the-new-general-2d-model-of-a-class-of-hh4lz90jjj.pdf

Robust stability of the new general 2D model of a class of continuous-discrete linear systems

New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete linear systems described by the general 2D model are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on examples.

/pdf/stability-of-continuous-discrete-linear-systems-described-by-1gd7zq9wpr.pdf

Stability of continuous-discrete linear systems described by the general model

Recently a dynamical development of the fractional and specially positive fractional linear systems theory has been observed. A dynamical system is called positive if and only if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. Variety of models having positive linear behavior can be found in engineering, management sciences, economics, social sciences, biology and medicine, etc.. An overview of state of the art in positive and fractional systems theory is given in monographs [1–5]. New class of 2D continuous-discrete linear systems has been introduced in [6, 7] and of positive fractional 2D hybrid linear systems in [3, 8]. Stability and robust stability of the general 2D model of a class of continuous-discrete linear systems has been analyzed in [9–11]. Stability, controllability and observability of 2D continuous-discrete linear systems have been investigated in [2, 6, 12–14]. Solvability of 2D hybrid linear systems has been addressed in [15, 16]. In this paper a new class of positive fractional 2D continuous-discrete linear systems is introduced. The solution to the state equations describing the systems is derived and the necessary and sufficient conditions for the positivity of the system is established. The paper is organized as follows. In Sec. 2 the solution to the equations describing the new class of fractional 2D continuous-discrete linear systems is derived. Necessary and sufficient conditions for the positivity of the fractional system are established in Sec. 3. Concluding remarks are given in Sec. 4. The following notation is used in this paper. The set of real n×m matrices is denoted by R and the set of n×m real matrices with nonnegative entries will be denoted R + (R+ = R n×1 + ). The n× n identity matrix will be denoted by In.

/pdf/positive-fractional-2d-continuous-discrete-linear-systems-jfoyb7sty4.pdf

Positive fractional 2D continuous-discrete linear systems

/pdf/improved-stability-and-robust-stability-conditions-for-a-2d3iet4w3d.pdf

Improved stability and robust stability conditions for a general model of scalar continuous-discrete linear systems

Purpose – The purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.Design/methodology/approach – Computation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.Findings – In this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.Originality/value – Presented methods are a new way for computing the solution of singular 2D hybrid linear systems.

Solution of 2D singular hybrid linear system

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Lukasz Sajewski

Author Tools

Chat about Author

Papers

Solution of 2D singular hybrid linear system