This paper is concerned with the zeros of sampled-data systems resulting from continuous-time systems preceded by a hold and followed by a sampler. The holds we shall consider are a zero-order hold and a first-order hold. For sufficiently small or large sampling periods, such zeros are called limiting zeros. For sufficiently small sampling periods, they are known to consist of two different types of zeros: the zeros of the first type correspond to the zeros of the original continuous-time system, while those of the second type have no continuous-time counterparts. We first show basic properties of the zeros of sample-data systems for sufficiently small sampling periods. Next, we clarify, in more detail, the correspondence between the former-type zeros of the sampled-data systems and the zeros of the original continuous-time system, including the stability property of these zeros. We also study stability properties of the latter-type zeros. In addition, we study limiting zeros for sufficiently large sampli...

Stability of the limiting zeros of sampled-data systems with zero-and first-order holds

The famous /spl Aring/strom-Hagander-Sternby theorem (1984) on limiting zeros of the pulse transfer function is extended by determining the accuracy of the asymptotic results for both the discretization and the intrinsic zeros when the sampling interval is small. Closed form formulas are derived that express the degree of the principal term of Taylor expansion of the difference between the true zeros and asymptotic ones as a function of the relative degree of the underlying continuous-time system and the value of the corresponding coefficient itself. Certain known results on asymptotic zeros are shown to be particular cases of the result presented.

On zeros of pulse transfer functions

This paper investigates the properties of the mapping from the simple zero /spl gamma/ of a scalar continuous-time system to the corresponding zero /spl Gamma/(T) of the sampled-data system that results by its discretization using a zero-order hold, where T is the sampling period. It is shown that /spl Gamma/(T) admits a Taylor expansion with respect to T, and that it coincides with that of exp(/spl gamma/T) at least up to the second-order term, in general, and at least up to the third-order term if the relative degree of the continuous-time system is greater than or equal to two. The result is applied to derive a new stability condition of /spl Gamma/(T) for sufficiently small sampling periods.

/pdf/analytic-study-on-the-intrinsic-zeros-of-sampled-data-3uwjuyw1w4.pdf

Analytic study on the intrinsic zeros of sampled-data systems

The Astrom-Hagander-Sternby theorem (1984) on asymptotic zeros of the pulse transfer function is extended by determining the accuracy of the asymptotic results for both the sampling and the intrinsic zeros when the sampling interval is small. Closed form formulae are derived that express the degree of the principal term of Taylor expansion of the difference between the true zeros and asymptotic ones as a function of the relative degree of the underlying continuous-time system, and the value of the corresponding coefficient itself. The results are illustrated by an example.

http://ieeexplore.ieee.org/iel4/4827/13355/00612051.pdf

On zeros of sampled systems

Frequency-domain method for H 2 optimization of time-delayed sampled-data systems

A relationship between real poles and real zeros of SISO (single-input, single-output) sampled data systems is presented, which is independent of the sampling period. The relation is stated in terms of a parity property involving the number of real zeros between any two real poles. This property allows the investigation of conditions for the preservation of stable or unstable zeros under sampling. A sufficient condition for stability of a sampled system with a continuous-time plant having all real zeros, and a sufficient condition for instability of a two-sampled system with an unstable plant is developed. >

https://ieeexplore.ieee.org/iel4/9/916/00024233.pdf

The relationship between real poles and real zeros in SISO sampled data systems

A digital control system with computational time delay is considered, in which the controlled plant is a continuous-time linear system and the control input is calculated by a digital computer based on the data of the output, measured before a certain time not greater than the sampling period. Some qualitative properties of the zeros, such as the characteristics of the limiting zeros, the parity relation between real poles and zeros, and the behaviour of the zeros with respect to the computational time delay are investigated, and the parity interlacing property and its dual are derived. A method of stabilization by a stable digital compensator using the inter-sample data is also proposed. Finally, the first-order hold case is discussed.

Properties of zeros in digital control systems with computational time delay

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.

H. Katori

Author Tools

Chat about Author

Papers

The relationship between real poles and real zeros in SISO sampled data systems

Properties of zeros in digital control systems with computational time delay