Nguyen Khoa Son
Emeritus Professor

Cộng tác viên
Research interests: Robust stability and Controlability


Address
Office: Building A2
Tel: +84 (0)4 37563474
Email: nkson AT math.ac.vn nkson AT vast.vn

Born in  Hue in  1948

Education and academic degrees:

  • 1972: Bachelor/Master: State University of Kharkov, Ukraine
  • 1978: PhD,  State University of Kharkov, Ukraine
  • 1990: Dr. habil., Institute of Mathematics, Polish Academy of Sciences, Warsaw
  • 1991: Associate Professor
  • 1996: Full Professor

 

Positions:

  • Deputy Director, Institute of Mathematics, 1995-1998
  • Vice-Director General, National Centre for Natural Sciences and Technology, 2001-2004
  • Vice-President, Vietnam Academy of Science and Technology, 2004-2008
  • Editor-in-Chief, Vietnam Journal of Mathematics, 1997-2011
  • Chairman of Steering Board, Research program for space science and technology (2008-2011, 2012-2015) 

 

Research areas: differential equations, optimization and control theory

 

 

PUBLICATIONS

List of publications in MathSciNet

 

List of recent publications
1Nguyen Khoa Son, Le Van Ngoc, Robustness of exponential stability of a class of switched positive linear systems with time delays, International Journal of Robust and Nonlinear Control, 34 (2024), no. 4, 2906–2926, (SCI-E, Scopus).
2Nguyen Khoa Son, Le Trung Hieu, Cao Thanh Tinh, Do Duc Thuan, New criteria for exponential stability of a class of nonlinear continuous-time difference systems with delays, International Journal of Control, 96 (2023), 1650-1660, (SCI-E, Scopus).
3Nguyen Khoa Son, Le Van Ngoc, Exponential stability analysis for a class of switched nonlinear time-varying functional differential systems, Nonlinear Analysis: Hybrid Systems, 44 (2022), 17 pages, (SCI-E, Scopus).
4Nguyen Khoa Son, Nguyen Nang Thieu, Nguyen Dong Yen, On the solution existence for prox-regular perturbed sweeping processes, Journal of Nonlinear and Variational Analysis 5 (2021), no. 6, 851-863. (SCI-E, Scopus, Preprint: download here).
5Nguyen Khoa Son, Le Van Ngoc, On robust stability of switched linear systems, IET Control Theory \& Applications  14 No. 1 (2020), 19-29. (SCI-E, Scopus).
6Nguyen Khoa Son, Nguyen Thi Hong, On Structured Distance to Uncontrollability of General Linear Retarded Systems, Acta Mathematica Vietnamica volume 45, (2020), pages411–433, Scopus.
7Nguyen Khoa Son, Đỗ Đức Thuận, Controllability radii of linear systems with constrained controls under structured perturbations, SIAM Journal on Control and Optimization, 54 (2016), 2820–2843, SCI(-E); Scopus.
8Nguyen Khoa Son, Do Duc Thuan, Nguyen Thi Hong, Radius of approximate controllability of linear retarded systems under structured perturbations, Systems & Control Letters, 84 (2015), 13–20, SCI(-E), Scopus.
9Nguyen Khoa Son, Do Duc Thuan, The structured controllability radii of higher order systems, Linear Algebra and its Applications, 438 (2013), 2701 - 2716, SCI(-E); Scopus.
10Nguyen Khoa Son, Do Duc Thuan, The structured distance to non-surjectivity and its application to calculating the controllability radius of descriptor systems,  Journal of Mathematical Analysis and Applications, 388 (2012), 272–281, SCI(-E); Scopus.
11Nguyen Khoa Son, B. T. Anh and B. T. Quan, Robust stability of positive linear systems under fractional perturbations in infinite dimensional spaces,  Dynamics of Continuous, Discrete and Impulsive Systems,  Ser. A: Mathematical Analysis  18 (2011), 420 - 441, SCI(-E); Scopus.
12Nguyen Khoa Son, Do Duc Thuan, On the radius of surjectivity for rectangular matrices and its application to measuring stabilizability of linear systems under structured perturbations, Journal of Nonlinear and Convex Analy, 12 (2011), 441-453, SCI(-E); Scopus.
13Nguyen Khoa Son, D. D. Thuan, The structured controllability radii of higher order descriptor systems,  Vietnam Journal of Mathematics 38 (2010), 373 - 380, Scopus.
14Nguyen Khoa Son, B. T. Anh, Robust stability of a class of positive Quasi-polynomials in banach spaces, Mathematical Notes 88 (2010), 651 - 661, SCI(-E); Scopus.
15Nguyen Khoa Son, B. T. Anh, Robust stability of positive linear systems in Banach spaces, Journal of Difference Equations and Applications, 16 (2010), 1447 -- 1461, SCI(-E); Scopus.
16Nguyen Khoa Son, B. T. Anh, The robustness of strong stability of posititive homogeneous difference systems under parameter perturbations, Numerical Functional Analysis and Optimization, 31 (2010), 97 -- 111, SCI(-E); Scopus.
17Nguyen Khoa Son, D. D. Thuan, The structured distance to uncontrollability under multi-perturbations: an approach using multi-valued linear operators, Systems and Control Letters, 59 (2010), 476 -- 483, SCI(-E); Scopus.
18Nguyen Khoa Son, B. T. Anh, Robust stability of delay difference systems under fractional perturbations in infinite-dimensional spaces, International Journal of Control, 83 (2010), 498 -- 505, SCI(-E); Scopus.
19Bui The Anh, Nguyen Khoa Son, Duong Dang Xuan Thanh, Perron-Frobenius theorem for positive polynomial operators in Banach lattices, Positivity, 13 (2009), 709-716.
20Bui The Anh, Nguyen Khoa Son, Duong Dang Xuan Thanh, Stability radii of positive linear time-delay systems under fractional perturbations, Systems & control letters, 58 (2009), 155-159.
21Nguyen Khoa Son, B. T. Anh, Robust stability of Metzler operators under parameter perturbations, International Journal of Robust and Nonlinear control, 19 (2009), 1931 -- 1939.
22Nguyen Khoa Son, B. T. Anh, Stability radii of positive linear systems under fractional perturbations, Int. J. Robust & Nonlinear Control, 19 (2009), 1267 - 1277.
23Nguyen Khoa Son, Do Duc Thuan, Controllability radius of linear systems with perturbed control sets, Vietnam J. Math. 36 (2008), 239–251.
24B. T. Anh, Nguyen Khoa Son, D. D. X. Thanh, Stability radii of delay difference systems under affine parameter perturbations in infinite dimensional spaces, Appl. Math. Comput. 202 (2008), 562 - 570.
25Bui The Anh, Nguyen Khoa Son, Stability radii of positive higher order difference system in infinite dimensional spaces, Systems Control Lett. 57 (2008), 822 - 827.
26Bui The Anh, Nguyen Khoa Son, Stability radii of positive linear systems under affine parameter perturbations in infinite dimensional spaces, Positivity 12 (2008), 677 - 690.
27Nguyen Khoa Son, Do Duc Thuan, Controllability radius of linear systems under structured perturbations, Vietnam J. Math., 36 (2008), 473-479.
28B. T. Anh, Nguyen Khoa Son, and D. D. X. Thanh, Robust stability of Metzler operator and delay equation in $L^p([-h,0];X)$, Vietnam J. Math. 34 (2006), 357 - 368.
29Pham Huu Anh Ngoc, Nguyen Khoa Son, Stability radii of linear systems under multi-perturbations. Numer. Funct. Anal. Optim. 25 (2005), 221 - 238.
30Nguyen Khoa Son, N. D. Huy, Maximizing the stability radius of discrete-time linear positive systems by linear feedbacks, Vietnam J. Math. 33 (2005), 161 - 171.
31Pham Huu Anh Ngoc, Nguyen Khoa Son, Stability radii of positive linear functional differential equations under multi-perturbations, SIAM J. Control Optim. 43 (2005), 2278 - 2295.
32Nguyen Dinh Huy, Nguyen Khoa Son, Existence of solution for multi-valued integral equations, Vietnam J. Math. 32 (2004), 323 - 329.
33Nguyen Khoa Son, P. H. A. Ngoc, Stability radii of linear systems under multi-perturbations, Numer. Funct. Anal. Optim. 25 (2004), 221 - 238.
34D. Hinrichsen, Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radii of higher order positive difference systems, Systems Control Lett. 49 (2003), 377 - 388.
35Pham Huu Anh Ngoc, Nguyen Khoa Son, Stability radii of positive linear difference equations under affine parameter perturbations, Appl. Math. Comput. 134 (2003), 577 - 594.
36Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radii of linear discrete-time systems with delays, Vietnam J. Math. 29 (2001), N0 4, 379 - 384.
37Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radii of linear functional differential equations, Vietnam J. Math. 29 (2001), 85 - 89.
38Nguyen Khoa Son, P. H. A. Ngoc, Robust stability of linear functional differential equations, Adv. Stud. Contemp. Math. (Pusan) 3 (2001),  43 - 59.
39Nguyen Khoa Son, Pham Huu Anh Ngoc, Robust stability of positive linear time-delay systems under affine parameter perturbations. Acta Math. Vietnam. 24 (1999), 353 - 371.
40Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability of linear infinite-dimensional systems under affine and fractional perturbations. Vietnam J. Math. 27 (1999), 153 - 167.
41Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radius of linear delay systems, In: Proc. American Control Conference, San Diego, California, USA, June 1999, 815 - 817.
42Hinrichsen D., Nguyen Khoa Son, Stability radii of positive discrete-time systems. 3rd International Conference on Approximation and Optimization in the Caribbean (Puebla, 1995), 113–124, Aportaciones Mat. Comun., 24, Soc. Mat. Mexicana, México, 1998.
43Nguyen Khoa Son, D. Hinrichsen, $\mu$ analysis and robust stability of positive linear systems. Appl. Math. Comput. Sci. 8 (1998), N0 2, 253 - 268.
44Nguyen Khoa Son, Pham Huu Anh Ngoc, Complex stability radius of linear retarded systems. Vietnam J. Math. 26 (1998), 379 - 384.
45D. Hinrichsen, Nguyen Khoa Son, Stability radii of positive discrete-time systems under affine parameter perturbations, Int. J. for Nonlinear & Robust Control, 8 (1998), 1169 - 1188.
46A. Fischer, D. Hinrichsen, Nguyen Khoa Son, Stability radii of Metzler operators. Vietnam J. Math. 26 (1998) 147 - 162.
47Hinrichsen D, Nguyen Khoa Son, Stability radii of positive discrete-time systems. Proceedings of the 3rd International Conference on Approximation and Optimization in the Caribbean (Puebla, 1995), 13 pp. (electronic), Benemérita Univ. Autón. Puebla, Puebla, 1997.
48Nguyen Khoa Son, Approximate controllability with positive controls. Acta Math. Vietnam. 22 (1997), 589 - 620.
49Nguyen Dinh Huy, Nguyen Khoa Son, On the existence of solutions to functional differential inclusions with boundary values. Vietnam J. Math. 25 (1997), 331 - 340.
50Nguyen Khoa Son, D. Hinrichsen, Robust stability positive continuous time systems. Numer. Funct. Anal. Optim. 17 (1996), 649 - 659.
51Nguyen Khoa Son, D. Hinrichsen, $\mu$-values analysis and stability radii of positive systems under block-diagonal affine perturbations, In: Proc. International Symposium on Automation and Robotics, Szeszin, August 1 - 6, 1996, Poland, 256 - 266.
52Diederich Hinrichsen, Nguyen Khoa Son, On structured singular values and robust stability radii of systems under affine perturbations. Vietnam J. Math. 1 (1996), 112 - 117.
53Nguyen Dinh Huy, Nguyen Khoa Son, Existence and relaxation of solutions of functional differential inclusions. Vietnam J. Math. 2 (1995), 279 - 291.
54Nguyen Khoa Son, D. Hinrichsen, Stability radii of positive dynamical systems, In: Proceedings of Inter. Congress of Industrial and Applied Mathematics, ICIAM'95, Hamburg, FRG, July 3-9, 1995, Zeitschrift fur Angewandte Mathematik und Mechanik, ZAMM, Vol. 2 : Applied Analysis, 756 - 758.
55Nguyen Khoa Son, D. Hinrichsen, Robust stability of positive linear systems, In: Proceedings of the 34th IEEE Conference on Control and Decision, New Orleans, USA, 1995, 1423 - 1425.
56Nguyen Khoa Son, On the real stability radius of positive linear discrete-time systems. Numer. Funct. Anal. Optim. 16 (1995).
57Nguyen Khoa Son, On the real stability radius of positive linear systems. Vietnam J. Math 23 (1995), 151 - 155.
58Nguyen Khoa Son, On the existence for positive eigenvalues of convex set-valued maps. Vietnam J. Math. 22 (1994), 109 - 113.
59Nguyen Khoa Son, Dynamical systems with state and control constraints: controllability and related topics. Vietnam J. Math. 21 (1993), 1 - 35.
60Nguyen Khoa Son, Nguyen Dinh Huy, On the qualitative properties of the solution set to functional differential inclusions in Banach spaces. Vietnam J. Math. 19 (1991), 43 - 58.
61Nguyen Khoa Son, D. Hinrichsen, The complex stability radii of discrete-time systems and simpletic pencils. Int. J. of Nonlinear & Robust Control, 1 (1991), 79 - 91.
62Nguyen Dinh Huy, Nguyen Khoa Son, On the existence of solutions for functional differential inclusions in Banach spaces. Acta Math. Vietnam. 16 (1991), 46 - 60.
63Nguyen Khoa Son, Constrained controllability of infinite dimensional systems with applications. Dr. Sc. Thesis. Institute of Mathematics, PAN, Warsaw, 1990.
64Nguyen Khoa Son, A unified approach to constrained approximate controllability for the heat equations and the retarded equations. J. Math. Anal. Appl. 159 (1990), 1 - 19.
65Nguyen Khoa Son, Approximate controllability with positive controls for linear retarded systems: a discrete-time approach. System modelling and optimization (Leipzig, 1989), 403–412, Lecture Notes in Control and Inform. Sci., 143, Springer, Berlin, 1990.
66Vu Ngoc Phat, Nguyen Khoa Son, Linear nonstationary discrete-time systems: Null controllability with restrained controls in Banach spaces. Optimization. 2 (1990), 271 - 279.
67D. Hinrichsen, Nguyen Khoa Son, Stability radius of discrete-time systems and simpletic pencils. In: Proceedings of the 28th IEEE Conference on Control and Decision, Tampa, USA, 1989, 2265 - 2270.
68Nguyen Khoa Son, Some remarks on the global controllability of linear discrete-time systems with bounded controls. Bollet. Uni. Mat. Italiana, Anal. Funz. Appl., Serie VI, V (1986), 245 - 254.
69Nguyen Khoa Son, Nguyen Van Su, Linear periodic systems : Controllability with restrained controls. Appl. Math. Optim. 14 (1986), 173 - 195.
70Nguyen Khoa Son, On the null-controllability of linear discrete-time systems with restrained controls. J. Optim. Theory Appl. 50 (1986), 313 - 329.
71Nguyen Khoa Son, Le Thanh, On the null-controllability of infinite dimensional discrete-time systems. Acta Math. Vietnam. 10 (1985), 3 - 14.
72Nguyen Khoa Son, Global controllability of linear autonomous systems: a geometric consideration. Systems Control Lett. 6 (1985), 207 - 212.
73Nguyen Khoa Son, Linear systems with state constraints in Banach spaces. Acta Math. Vietnam. 7 (1982), 71 - 85.
74Nguyen Khoa Son, Controllability of linear discrete-time systems with constrained controls in Banach spaces. Control and Cybern. 10 (1981), 5 - 16.
75Nguyen Khoa Son, $\sigma$ controllability of linear autonomous systems with constraints on controls. Differ. Uravnenia 16 (1980), 394 - 404 (in Russian).
76 Korobov. V. I, Nguyen Khoa Son, Controllability of linear systems in a Banach space in the presence of constraints on controls, II. Differ. Uravnenia 16 (1980), 1010 - 1022 (in Russian).
77 Korobov. V. I, Nguyen Khoa Son, Controllability of linear systems in a Banach space in the presence of constraints on controls, I. Differ. Uravnenia 16 (1980), 806 - 817 (in Russian).
78Nguyen Khoa Son, Local controllability of linear systems with restrained controls in Banach space.  Acta Math. Vietnam. 5 (1980), 78 - 87.
79Nguyen Khoa Son, Controllability of dynamical systems in the presence of constraints on controls. Ph. D. Thesis, Kharkov University, 1978, Kharkov (in Russian).
80Nguyen Khoa Son, Controllability of nonlinear systems with damped perturbations. Vestnik Kharkov Univ. 43 (1978), 21 - 34 (in Russian).
Preprints
1Nguyen Khoa Son, Le Trung Hieu, Cao Thanh Tinh, Do Duc Thuan, New criteria for exponential stability of a class of nonlinear continuous-time difference systems with delays, International Journal of Control, 95 (2022), 11 pages.