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Topic · Control and Systems Engineering

Stability and Controllability of Differential Equations

Stability and Controllability of Differential Equations is a research topic within Control and Systems Engineering. Science Explorer counts 31k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the analysis and control of distributed parameter systems, particularly emphasizing boundary control, stability, wave equations, attractors, feedback control, hyperbolic partial differential equations (PDEs), viscoelasticity, global existence, and controllability.

  • Distributed Parameter Systems
  • Boundary Control
  • Stability
  • Wave Equations
  • Attractors
  • Feedback Control
  • Hyperbolic PDEs
  • Viscoelasticity
  • Global Existence
  • Controllability
Research works
31k
fractional, since 1950
In the world top 10%
3.1k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+3%
the tick is no change
Largest producer
China
50% of the 10 largest, 2022-now
Stability and Controllability of Differential Equations

Which countries lead Stability and Controllability of Differential Equations research?

By volume, China and the United States publish the most (1.9k and 328 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.9k works
  2. 2 United States 328 works
  3. 3 France 319 works
  4. 4 Russia 227 works
  5. 5 Brazil 191 works
  6. 6 India 178 works
  7. 7 Germany 167 works
  8. 8 Italy 159 works
  9. 9 Algeria 152 works
  10. 10 Morocco 143 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 50.2%United States: 8.8%France: 8.5%Russia: 6.1%6 others listed: 26.5%50%largest
China1,877 · 50.2%United States328 · 8.8%France319 · 8.5%Russia227 · 6.1%6 others listed990 · 26.5%

Shares of the rows listed above, not of the whole node.

Which institutions lead Stability and Controllability of Differential Equations research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Stability and Controllability of Differential Equations research, followed by Russian Academy of Sciences and Southwest University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 149 works
  2. 2 Russian Academy of SciencesRussia 64 works
  3. 3 Southwest UniversityChina 39 works
  4. 4 Beijing Institute of TechnologyChina 33 works
  5. 5 Northwest Normal UniversityChina 33 works
  6. 6 Harbin Institute of TechnologyChina 30 works
  7. 7 Central South UniversityChina 30 works
  8. 8 Chinese Academy of SciencesChina 28 works
  9. 9 Shanxi UniversityChina 28 works
  10. 10 Vellore Institute of Technology UniversityIndia 27 works

Who are the leading researchers in Stability and Controllability of Differential Equations?

The most-cited researchers publishing on Stability and Controllability of Differential Equations include Stephen Boyd, John H. Seinfeld and Tasawar Hayat.

  1. 1 Stephen Boyd United States 142k citations
  2. 2 John H. Seinfeld United States 140k citations
  3. 3 Tasawar Hayat Pakistan 135k citations
  4. 4 Jin Li China 132k citations
  5. 5 Jing Li United States 120k citations
  6. 6 Stanley Osher United States 119k citations
  7. 7 Guanrong Chen China 116k citations
  8. 8 Kang Xu United States 112k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Stability and Controllability of Differential Equations?

The most cited paper in Stability and Controllability of Differential Equations is "User’s guide to viscosity solutions of second order partial differential equations" (Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions, 1992), with 5,020 citations. Next come "Compact sets in the spaceL p (O,T; B)" (4,138) and "Predictive control with constraints" (3,550).

Most cited papers
#PaperReleasedCitations
1 User’s guide to viscosity solutions of second order partial differential equations Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions · Bulletin of the American Mathematical Society Open access 1992 5,020
2 Compact sets in the spaceL p (O,T; B) Jacques Simon · Annali di Matematica Pura ed Applicata (1923 -) Open access Dec 1986 4,138
3 Predictive control with constraints Eduardo Fernández Camacho · Automatica 30 Apr 2003 3,550
4 Feedback control of dynamic systems Stephen Kahne · Automatica May 1987 3,473
5 Smooth stabilization implies coprime factorization Eduardo D. Sontag · IEEE Transactions on Automatic Control Apr 1989 2,751
All 99 most cited papers, with filters and sorting

Where is Stability and Controllability of Differential Equations research done?

The largest centres of Stability and Controllability of Differential Equations research in 2022-now are Beijing (China), Shanghai (China), Nanjing (China) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Meknes and Qufu.

Largest cities, 2022-now

  1. 1 BeijingChina 199 works
  2. 2 ShanghaiChina 113 works
  3. 3 NanjingChina 101 works
  4. 4 ParisFrance 92 works
  5. 5 MoscowRussia 86 works
  6. 6 ChengduChina 75 works
  7. 7 GuangzhouChina 74 works
  8. 8 ChangshaChina 73 works
  9. 9 ChongqingChina 70 works
  10. 10 JinanChina 70 works

Where it is the local speciality

  1. MeknesMA · 23.8 works31×
  2. QufuCN · 22.5 works23×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Stability and Controllability of Differential Equations than the world average.

See Stability and Controllability of Differential Equations on the map

Where is the best place to study Stability and Controllability of Differential Equations?

Among universities, judged by research, Vellore Institute of Technology University, Universidad de Sevilla and Qassim University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 19.34%fractional works in this field (log) →share of work in the world top 10% →Vellore Institute of…Universidad de SevillaQassim UniversityBeijing Institute of…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Vellore Institute of Technology UniversityIndia 82.242.6%6.1×27 +418.5%
2Universidad de SevillaSpain 57.418.5%8.9×23 +11.4%
3Qassim UniversitySaudi Arabia 56.518.1%20.0×23 +0.6%
4Beijing Institute of TechnologyChina 56.310.3%6.3×33 +37.8%
5Southwest UniversityChina 56.211.2%16.1×39 +0.8%
6University of California San DiegoUnited States 55.539.2%4.1×18 -14.8%
7Université Paris-SaclayFrance 54.112.3%7.4×21 +30.4%
8Northwest Normal UniversityChina 54.07.3%31.2×33 +50.2%
9Central South UniversityChina 53.513.6%3.5×30 +105.3%
10Hunan Normal UniversityChina 53.320.3%18.5×19 +46.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Stability and Controllability of Differential Equations, country by country

Is Stability and Controllability of Differential Equations research growing?

Output in 2022-2025 was 3% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Stability and Controllability of Differential Equations.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Stability and Controllability of Differential Equations as a percentage of every work published that year, 0.020% in 2024.

still counting0.020%0.040%0.060%Stability and Controllability of Differential Equations0.020% in 202519801990200020102020

Fractional works of Stability and Controllability of Differential Equations over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Stability and Controllability of Differential Equations9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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