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, 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).
2Nguyen 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).
3Nguyen 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).
4Nguyen Khoa Son, Nguyen Thi Hong, On Structured Distance to Uncontrollability of General Linear Retarded Systems, Acta Mathematica Vietnamica volume 45, (2020), pages411–433, Scopus.
5Nguyen 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.
6Nguyen 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.
7Nguyen 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.
8Nguyen 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.
9Nguyen 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.
10Nguyen 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.
11Nguyen Khoa Son, D. D. Thuan, The structured controllability radii of higher order descriptor systems,  Vietnam Journal of Mathematics 38 (2010), 373 - 380, Scopus.
12Nguyen 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.
13Nguyen 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.
14Nguyen 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.
15Nguyen 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.
16Nguyen 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.
17Bui The Anh, Nguyen Khoa Son, Duong Dang Xuan Thanh, Perron-Frobenius theorem for positive polynomial operators in Banach lattices, Positivity, 13 (2009), 709-716.
18Bui 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.
19Nguyen Khoa Son, B. T. Anh, Robust stability of Metzler operators under parameter perturbations, International Journal of Robust and Nonlinear control, 19 (2009), 1931 -- 1939.
20Nguyen Khoa Son, B. T. Anh, Stability radii of positive linear systems under fractional perturbations, Int. J. Robust & Nonlinear Control, 19 (2009), 1267 - 1277.
21Nguyen Khoa Son, Do Duc Thuan, Controllability radius of linear systems with perturbed control sets, Vietnam J. Math. 36 (2008), 239–251.
22B. 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.
23Bui The Anh, Nguyen Khoa Son, Stability radii of positive higher order difference system in infinite dimensional spaces, Systems Control Lett. 57 (2008), 822 - 827.
24Bui The Anh, Nguyen Khoa Son, Stability radii of positive linear systems under affine parameter perturbations in infinite dimensional spaces, Positivity 12 (2008), 677 - 690.
25Nguyen Khoa Son, Do Duc Thuan, Controllability radius of linear systems under structured perturbations, Vietnam J. Math., 36 (2008), 473-479.
26B. 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.
27Pham Huu Anh Ngoc, Nguyen Khoa Son, Stability radii of linear systems under multi-perturbations. Numer. Funct. Anal. Optim. 25 (2005), 221 - 238.
28Nguyen 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.
29Pham 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.
30Nguyen Dinh Huy, Nguyen Khoa Son, Existence of solution for multi-valued integral equations, Vietnam J. Math. 32 (2004), 323 - 329.
31Nguyen Khoa Son, P. H. A. Ngoc, Stability radii of linear systems under multi-perturbations, Numer. Funct. Anal. Optim. 25 (2004), 221 - 238.
32D. Hinrichsen, Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radii of higher order positive difference systems, Systems Control Lett. 49 (2003), 377 - 388.
33Pham Huu Anh Ngoc, Nguyen Khoa Son, Stability radii of positive linear difference equations under affine parameter perturbations, Appl. Math. Comput. 134 (2003), 577 - 594.
34Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radii of linear discrete-time systems with delays, Vietnam J. Math. 29 (2001), N0 4, 379 - 384.
35Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability radii of linear functional differential equations, Vietnam J. Math. 29 (2001), 85 - 89.
36Nguyen Khoa Son, P. H. A. Ngoc, Robust stability of linear functional differential equations, Adv. Stud. Contemp. Math. (Pusan) 3 (2001),  43 - 59.
37Nguyen 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.
38Nguyen Khoa Son, Pham Huu Anh Ngoc, Stability of linear infinite-dimensional systems under affine and fractional perturbations. Vietnam J. Math. 27 (1999), 153 - 167.
39Nguyen 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.
40Hinrichsen 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.
41Nguyen Khoa Son, D. Hinrichsen, $\mu$ analysis and robust stability of positive linear systems. Appl. Math. Comput. Sci. 8 (1998), N0 2, 253 - 268.
42Nguyen Khoa Son, Pham Huu Anh Ngoc, Complex stability radius of linear retarded systems. Vietnam J. Math. 26 (1998), 379 - 384.
43D. 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.
44A. Fischer, D. Hinrichsen, Nguyen Khoa Son, Stability radii of Metzler operators. Vietnam J. Math. 26 (1998) 147 - 162.
45Hinrichsen 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.
46Nguyen Khoa Son, Approximate controllability with positive controls. Acta Math. Vietnam. 22 (1997), 589 - 620.
47Nguyen Dinh Huy, Nguyen Khoa Son, On the existence of solutions to functional differential inclusions with boundary values. Vietnam J. Math. 25 (1997), 331 - 340.
48Nguyen Khoa Son, D. Hinrichsen, Robust stability positive continuous time systems. Numer. Funct. Anal. Optim. 17 (1996), 649 - 659.
49Nguyen 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.
50Diederich Hinrichsen, Nguyen Khoa Son, On structured singular values and robust stability radii of systems under affine perturbations. Vietnam J. Math. 1 (1996), 112 - 117.
51Nguyen Dinh Huy, Nguyen Khoa Son, Existence and relaxation of solutions of functional differential inclusions. Vietnam J. Math. 2 (1995), 279 - 291.
52Nguyen 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.
53Nguyen 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.
54Nguyen Khoa Son, On the real stability radius of positive linear discrete-time systems. Numer. Funct. Anal. Optim. 16 (1995).
55Nguyen Khoa Son, On the real stability radius of positive linear systems. Vietnam J. Math 23 (1995), 151 - 155.
56Nguyen Khoa Son, On the existence for positive eigenvalues of convex set-valued maps. Vietnam J. Math. 22 (1994), 109 - 113.
57Nguyen Khoa Son, Dynamical systems with state and control constraints: controllability and related topics. Vietnam J. Math. 21 (1993), 1 - 35.
58Nguyen 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.
59Nguyen 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.
60Nguyen Dinh Huy, Nguyen Khoa Son, On the existence of solutions for functional differential inclusions in Banach spaces. Acta Math. Vietnam. 16 (1991), 46 - 60.
61Nguyen Khoa Son, Constrained controllability of infinite dimensional systems with applications. Dr. Sc. Thesis. Institute of Mathematics, PAN, Warsaw, 1990.
62Nguyen 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.
63Nguyen 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.
64Vu Ngoc Phat, Nguyen Khoa Son, Linear nonstationary discrete-time systems: Null controllability with restrained controls in Banach spaces. Optimization. 2 (1990), 271 - 279.
65D. 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.
66Nguyen 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.
67Nguyen Khoa Son, Nguyen Van Su, Linear periodic systems : Controllability with restrained controls. Appl. Math. Optim. 14 (1986), 173 - 195.
68Nguyen Khoa Son, On the null-controllability of linear discrete-time systems with restrained controls. J. Optim. Theory Appl. 50 (1986), 313 - 329.
69Nguyen Khoa Son, Le Thanh, On the null-controllability of infinite dimensional discrete-time systems. Acta Math. Vietnam. 10 (1985), 3 - 14.
70Nguyen Khoa Son, Global controllability of linear autonomous systems: a geometric consideration. Systems Control Lett. 6 (1985), 207 - 212.
71Nguyen Khoa Son, Linear systems with state constraints in Banach spaces. Acta Math. Vietnam. 7 (1982), 71 - 85.
72Nguyen Khoa Son, Controllability of linear discrete-time systems with constrained controls in Banach spaces. Control and Cybern. 10 (1981), 5 - 16.
73Nguyen Khoa Son, $\sigma$ controllability of linear autonomous systems with constraints on controls. Differ. Uravnenia 16 (1980), 394 - 404 (in Russian).
74 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).
75 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).
76Nguyen Khoa Son, Local controllability of linear systems with restrained controls in Banach space.  Acta Math. Vietnam. 5 (1980), 78 - 87.
77Nguyen Khoa Son, Controllability of dynamical systems in the presence of constraints on controls. Ph. D. Thesis, Kharkov University, 1978, Kharkov (in Russian).
78Nguyen 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.