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All Journal Journal on Mathematics Education (JME) Journal on Mathematics Education (JME) SITEKIN: Jurnal Sains, Teknologi dan Industri Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Math Educa Journal Jurnal Matematika UNAND Mandalika Mathematics and Educations Journal Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika
Muhafzan Muhafzan
Departemen Matematika Dan Sains Data, FMIPA Universitas Andalas
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Transportation Other

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STABILITY ANALYSIS AND PERFORMANCE OF KALMAN FILTERING AND ROBUST KALMAN FILTERING ON UNCERTAIN CONTINUOUS-TIME SYSTEMS Rudianto, Budi; Muhafzan, Muhafzan; Syafwan, Mahdhivan; Sy, Syafrizal
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp1295-1306

Abstract

This paper discusses the stability analysis of robust Kalman filtering on uncertain continuous-time systems. In real applications, systems often face model uncertainty and noise affecting prediction and estimation accuracy. Therefore, a filtering method is needed to overcome these uncertainties. Robust Kalman filtering is one of the most effective methods for dealing with model uncertainty. In this paper, we discuss the application of this method to continuous-time systems and its stability analysis. Simulation results show that robust Kalman filtering can provide more accurate and stable estimates than the conventional Kalman filter. Robust Kalman filtering can reduce the estimation error to about 30% under uncertain model conditions and maintain stability despite disturbances of up to 20% of the system parameters. However, this research has limitations regarding testing scenarios with more complex uncertainty models and higher disturbance variability. The originality of this research lies in its focus on the stability analysis of robust Kalman filtering on uncertain continuous-time systems, which has rarely been discussed in depth in previous literature.
SOME MODIFICATIONS OF CHEBYSHEV-HALLEY’S METHODS FREE FROM SECOND DERIVATIVE WITH EIGHTH-ORDER OF CONVERGENCE Muda, Yuslenita; Santi, Neng; Wartono, Wartono; Muhafzan, Muhafzan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (501.493 KB) | DOI: 10.30598/barekengvol16iss2pp531-538

Abstract

The variant of Chebyshev-Halley’s method is an iterative method used for solving a nonlinear equation with third order of convergence. In this paper, we present some new variants of three steps Chebyshev-Halley’s method free from second derivative with two parameters. The proposed methods have eighth-order of convergence for and and require four evaluations of functions per iteration with index efficiency equal to . Numerical simulation will be presented by using several functions to show the performance of the proposed methods.
KESTABILAN MODEL NICHOLSON-BAILEY Oktaviani, Mira; ZULAKMAL, ZULAKMAL; MUHAFZAN, MUHAFZAN
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.144-152.2023

Abstract

Dalammakalahinidikajikestabilan Model Nicholson-Bailey yang mempelajaritentanginteraksiantarainangdanparasit. Model Nicholson-Bailey digambarkandalambentukpersamaanbeda non linierdiskrit. Darihasilanalisisdiperolehduatitiktetap yang kestabilannyaditentukanolehtingkatreproduksiinang. Sebagaihasilutamadarimakalahini, disajikan suatusyaratperludancukupuntukkestabilanasimtotikdarititiktetap model Nicholson-Bailey.
LOCAL STABILITY OF THE SEIQR EPIDEMIC MODEL APPLIED TO COVID-19 SPREAD CASES Muhafzan, Muhafzan; Monika, Indah; Baqi, Ahmad Iqbal; Narwen, Narwen; Zulakmal, Zulakmal
Jurnal Matematika UNAND Vol. 15 No. 1 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.1.123-131.2026

Abstract

Pandemi COVID-19 telah memberikan dampak signifikan secara global, menuntut pemahaman yang mendalam mengenai dinamika penyebarannya untuk menentukan langkah intervensi yang efektif. Penelitian ini membahas analisis kestabilan model epidemi SEIQR (Susceptible, Exposed, Infectious, Quarantined, Recovered), yang merupakan pengembangan dari model SIR standar dengan penambahan kompartemen karantina ($Q$) dan masa inkubasi ($E$). Model ini dirancang untuk merepresentasikan kebijakan isolasi mandiri atau karantina rumah sakit yang diterapkan selama pandemi. Metode yang digunakan dalam penelitian ini meliputi pembentukan sistem persamaan diferensial non-linear, penentuan titik ekuilibrium (bebas penyakit dan endemik), serta perhitungan Bilangan Reproduksi Dasar menggunakan metode Next-Generation Matrix. Analisis kestabilan lokal dilakukan dengan menggunakan linearisasi di sekitar titik ekuilibrium dan kriteria Routh-Hurwitz. Hasil analisis menunjukkan bahwa penyebaran COVID-19 akan menghilang jika $\Re_0 < 1$, yang berarti titik ekuilibrium bebas penyakit bersifat stabil asimtotik. Sebaliknya, jika $\Re_0 > 1$, penyakit akan menetap dalam populasi dan mencapai titik ekuilibrium endemik yang stabil. Simulasi numerik disertakan untuk memvalidasi hasil analisis teoritis dan menunjukkan bahwa efektivitas karantina memiliki peran krusial dalam menekan nilai $\Re_0$ dan mempercepat laju pemulihan populasi.
RAINBOW CONNECTION NUMBERS IN GRAPHS: A COMPREHENSIVE STUDY Gema Hista Medika; Syafrizal Sy; Muhafzan Muhafzan; Zulfaneti Zulfaneti
Math Educa Journal Vol 10, No 1 (2026)
Publisher : UIN Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/mej.v10i1.13681

Abstract

The rainbow connection number is a graph parameter that integrates edge colouring and graph connectivity. A connected graph is said to be rainbow connected if every pair of vertices is joined by a path whose edges have distinct colours, and the rainbow connection number represents the minimum number of colours required to satisfy this property. This study aims to provide a comprehensive and systematic analysis of research developments related to rainbow connection numbers in graphs. The method employed is a systematic literature review of reputable international journals and nationally accredited publications. The analysis covers fundamental definitions, known values for various classes of graphs, relationships with structural parameters such as diameter, minimum degree, and connectivity, as well as computational complexity and several important variants, including strong rainbow connection, rainbow vertex-connection, and total rainbow connection. The results indicate that the rainbow connection number is strongly influenced by graph structure, with diameter serving as a natural lower bound and connectivity contributing to tighter upper bounds. Furthermore, determining the exact value for general graphs is computationally intractable, motivating the use of approximation and heuristic approaches. This study also identifies research gaps, particularly in algorithmic development and the analysis of complex graph class, and highlights potential applications in communication networks and network security.
Eksistensi dan Keunikan dalam Pengendalian LQ Berhorison Tak Terbatas Melalui Analisis Riccati Berbasis Sontag Budi Rudianto; Muhafzan Muhafzan; Mahdhivan Syafwan; Syafrizal Sy
Mandalika Mathematics and Educations Journal Vol 8 No 1 (2026): Edisi Maret
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v8i1.10782

Abstract

This paper examines the existence and uniqueness of solutions to Linear Quadratic (LQ) optimal control problems with infinite time horizons in time-varying dynamic systems. By extending Sontag's Theorem to semi-infinite intervals, the properties of The Riccati Differential Equation’s solutions are analyzed under assumptions of essential boundedness and boundedness of the system matrix and cost weights. It is proven that the Riccati matrix solution P(t) exists globally, remains positive definite, and converges to the steady-state limit P∞. The uniqueness of the optimal control–state pair (x,u) is obtained through P(t)-based co-state analysis. Simulations on satellite attitude control systems demonstrate convergence and robustness towards periodic disturbances, supporting applications in adaptive control, robust estimation, and time-varying filtering.
Co-Authors Alfi Yunita Amalina . Arrival Rince Putri Bahri, Susila Baqi, Ahmad Iqbal Baqi, Ahmad Iqbal Budi Rudianto Efendi Efendi FARRAS VITASHA PUTRI Gema Hista Medika Hamdunah Hanan, Hafizhah Atrya Hutagalung, Miya Qarlina Khairunnisa Khairunnisa Khairunnisa Khairunnisa Khofifa Ramadhani Luthfiah Khairunnisa Maidilla Iswari Mira Oktaviani Monika, Indah Narwen Narwen Noverina Alfiany Nurweni Putri Nurwijayanti Oktaviani, Mira RAHMI KHAIRUN NISA RINDI WULANDARI TANJUNG Santi, Neng Syafrizal Sy Syafrizal Sy, Syafrizal Syafwan, Mahdhivan Wartono Wartono YULANDA MARDIANA PUTRI Yuslenita Muda Zulakmal, Zulakmal Zulfaneti Zulfaneti Zulkardi Zulkardi Zulkardi Zulkardi