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Article Citation - WoS: 1Citation - Scopus: 1Novel Criterion for Stability of Discrete-Time Systems in a State-Space Realization Utilizing Saturation Nonlinearities(Elsevier Science inc, 2011) Singh, VimalA new criterion for the global asymptotic stability of discrete-time systems in a state-space realization utilizing saturation nonlinearities is presented. The form of the criterion is unconventional in that it offers the flexibility of using even an unsymmetric Lyapunov matrix P. A recently reported criterion is shown to be a special case of the present criterion. An example shows the effectiveness of the new criterion. (C) 2011 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3An Inverse Spectral Problem for Complex Jacobi Matrices(Elsevier, 2010) Guseinov, Gusein Sh.We introduce the concept of generalized spectral function for finite order complex Jacobi matrices and solve the inverse problem with respect to the generalized spectral function. The results obtained can be used for solving of initial-boundary value problems for finite nonlinear Toda lattices with the complex-valued initial conditions by means of the inverse spectral problem method. (C) 2009 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 7Solution of the Finite Complex Toda Lattice by the Method of Inverse Spectral Problem(Elsevier Science inc, 2013) Huseynov, Aydin; Guseinov, Gusein Sh.We show that the finite Toda lattice with complex-valued initial data can be integrated by the method of inverse spectral problem. For this goal spectral data for complex Jacobi matrices are introduced and an inverse spectral problem with respect to the spectral data is solved. The time evolution of the spectral data for the Jacobi matrix associated with the solution of the Toda lattice is computed. Using the solution of the inverse spectral problem with respect to the time-dependent spectral data we reconstruct the time-dependent Jacobi matrix and hence the desired solution of the finite complex Toda lattice. (C) 2012 Elsevier Inc. All rights reserved.
