In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.
References
Bellman R: Introduction to Matrix Analysis, McGraw Hill Book Company, Inc., New York, 1960.
Aurel Diamandescu, Existence of bounded solutions for a system of differential equations, Electronic J. of Differential Equations, vol. 2004, no. 63, p: 1-6 (2004).
Charyulu L. N. R., Sundaranand V. Putcha, G.V.S.R. Deekshitulu, Existence of -bounded solutions for linear system first order Kronecker product systems, Int. J. Recent Sci. Res., vol. 11, no. 6, p: 39047-39053 (2020).
Kasi Viswanadh V. Kanuri, K. N. Murty, “Three-Point boundary value problems associated with first order matrix difference system-existence and uniqueness via shortest and closest Lattice vector methods”, Journal of Nonlinear Sciences and Applications, Volume 12, Issue 11, (2019) 720–727.
Kasi Viswanadh V Kanuri, Existence Of Ψ-Bounded Solutions For Fuzzy Dynamical Systems On Time Scales, International Journal of Scientific & Engineering Research, 2020, Vol. 11, No. 5, 613--624.
Kasi Viswanadh V. Kanuri, R. Suryanarayana, K. N. Murty, Existence of Ψ-bounded solutions for linear differential systems on time scales, Journal of Mathematics and Computer Science, 20 (2020), no. 1, 1--13.
Murty, K. N., Andreou, S., Viswanadh, K. V. K., Qualitative properties of general first order matrix difference systems. Nonlinear Studies, 16(2009), no. 4, 359-370.
K. N. Murty, V. V. S. S. S. Balaram, K.V. K. Viswanadh, “Solution of Kronecker Product Initial Value Problems Associated with First Order Difference System via Tensor-based Hardness of the Shortest Vector Problem”, Electronic Modeling, vol. 6, p: 19-33 (2008).
K.N.Murty, K.R.Prasad, M.A.S.Srinivas, Upper and lower bounds for the solution of the general matrix Riccati differential equation, Journal of Mathematical Analysis and Applications, Vol 147, Iss. 1, 1990, PP 12--21
K.N. Murty, K.V.K. Viswanadh, P. Ramesh, Yan Wu, “Qualitative properties of a system of differential equation involving Kronecker product of matrices”, Nonlinear Studies, Vol 20, No: 3, P: 459--467 (2013)
K.N. Murty, Yan Wu, Viswanadh V. Kanuri, “Metrics that suit for dichotomy, well conditioning of object oriented design”, Nonlinear Studies, Vol 18, No: 4, P: 621--637 (2013).
Kasi Viswanadh V Kanuri, Y. Wu, K.N. Murty, “Existence of (Φ ⨂Ψ) bounded solution of linear first order Kronecker product of system of differential equations”, International Journal of Science and Engineering Research, 2020, Vol 11, No. 6, P: 721--730.
Kasi Viswanadh V Kanuri, K. N. Murty, P. Sailaja, “A New Approach to The Construction of a Transition Matrix with Several Applications to Control System Theory”, AIP Conference Proceedings, ICMM-757, December 2019 (In Press).
T. G. Halam, On asymptotic equivalence of the bounded solutions of two systems of differential equations, Mich. Math. J., vol. 16, no. 4, p:353-363, (1969.
Yan Wu, Sailaja P, K. N. Murty, Stability, controllability, and observability criteria for state-space dynamical systems on measure chains with an application to fixed point arithmetic, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 4, 187—195.
