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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Matematika UNAND Mandalika Mathematics and Educations Journal
Syafrizal Sy, Syafrizal
Universitas Andalas, Padang, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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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.
SOFT GRAPHS OF THE BARBELL STAR GRAPH Helmi, Monika Rianti; Sy, Syafrizal; Nazra, Admi; Muhafzan; Hanifa, Nurul; Alfiany, Noverina
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.366-375.2025

Abstract

\textit{Let $G^*=(V(G^*),E(G^*))$ is a simple graph and $A$ be a non-empty set of parameter. Let $R\subseteq A\times V(G^*)$ be a arbitrary relation from $A$ to $V(G^*)$. A mapping $F:A\to P(V(G^*))$ can be defined as $F(x)=\left\{y\in V\mid xRy \right\}$ and a mapping $K:A\to P(E(G^*))$ can be defined as $K(x)=\left\{uv\in E\mid \left\{u,v\right\}\subseteq F(x)\right\}$. A pair $(F,A)$ and $(K,A)$ are soft sets over $V(G^*)$ and $E(G^*)$ respectively, then $(F(a),K(a))$ is a subgraph of $G^*$. The 4-tuple $G=(G^*,F,K,A)$ is called a soft graph of $G$. In this paper, we enumerate soft graph of amalgamation of path and star.}
BILANGAN RAMSEY MULTIPARTIT HIMPUNAN (R-M-H) M_j(C_n, C_s) UNTUK CYCLE Majid, Abdul -; SY, SYAFRIZAL; NAZRA, ADMI
Jurnal Matematika UNAND Vol. 12 No. 4 (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.12.4.309-317.2023

Abstract

Diberikan dua graf G dan H sembarang. Bilangan Ramsey multipartit himpunan (R-M-H) M_j(G, H) dengan bilangan asli j ≥ 2, adalah bilangan bulat positif terkecil t sedemikian sehingga jika semua sisi dari graf multipartit seimbang lengkap K_{t×j} diberi sebarang 2−pewarnaan merah-biru, maka graf K_{t×j} senantiasa memuat G berwarna merah sebagai subgraf atau H berwarna biru sebagai subgraf. Graf C_n adalah suatu graf cycle dengan n ≥ 3 titik. Pada artikel ini, Penulis akan menentukan bilangan R-M-H M_j(C_n, C_s) untuk sebarang bilangan asli n ≥ 3 ganjil dan s ≥ 3. Hasil dari penelitian ini adalah ditemukannya bilangan R-M-H Mj (C_n, C_s) untuk cycle.
BILANGAN R-M-H UNTUK GRAF LINTASAN P_4 DAN GRAF RODA W_n DENGAN n>=3 Multasya, Nadya Citra; SYAFWAN, MAHDHIVAN; SY, SYAFRIZAL
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.12.2.135-143.2023

Abstract

Diberikan dua graf G dan H serta bilangan asli j>=2. Bilangan Ramsey multipartit himpunan (R-M-H) M_j(G,H) adalah suatu bilangan bulat positif terkecil t sedemikian sehingga untuk sebarang faktorisasi K_(txj) = F_1 + F_2 senantiasa F_1 memuat subgraf G atau F_2 memuat subgraf H. Pada artikel ini akan ditentukan M_3(P_4,W_n) dimana P_4 adalah suatu graf lintasan yang terdiri dari 4 simpul dan W_n adalah suatu graf roda yang terdiri dari n+1 simpul dengan n>=3.
Eksistensi dan Keunikan dalam Pengendalian LQ Berhorison Tak Terbatas Melalui Analisis Riccati Berbasis Sontag Rudianto, Budi; Muhafzan, Muhafzan; Syafwan, Mahdhivan; Sy, Syafrizal
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 Admi Nazra Alfiany, Noverina Budi Rudianto Hanifa, Nurul Helmi, Monika Rianti Majid, Abdul - Muhafzan Muhafzan Muhafzan Multasya, Nadya Citra Nurwijayanti Syafwan, Mahdhivan