Derong Liu's Top 10 Publications on Stability Analysis of Nonlinear Dynamical Systems

These publications made contributions to the field of stability analysis of nonlinear dynamical systems: (a) established global asymptotic stability results for dynamical systems with saturation-type nonlinearities and established results for the absence of limit cycles in digital filters employing generalized overflow arithmetic; (b) established necessary and sufficient conditions under which positive semi-definite matrices can be used to construct Lyapunov functions for dynamical systems with saturation-type nonlinearities; (c) established global asymptotic stability results for two-dimensional digital filters (described by Roesser model and by Fornasini-Marchesini model) employing generalized overflow arithmetic; (d) established global asymptotic stability results for dynamical systems with partial state saturation nonlinearities; and (e) established necessary and sufficient conditions for the robust absolute stability of nonlinear dynamical systems with time-varying nonlinearities.
  1. D. Liu and A. N. Michel, Dynamical Systems with Saturation Nonlinearities: Analysis and Design, New York: Springer-Verlag, 1994.
  2. D. Liu and A. N. Michel, "Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol.39, pp.798-807, Oct. 1992.
  3. D. Liu and A. N. Michel, "Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol.41, pp.127-137, Feb. 1994.
  4. D. Liu, "Lyapunov stability of two-dimensional digital filters with overflow nonlinearities," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol.45, pp.574-577, May 1998.
  5. D. Liu and A. N. Michel, "Stability analysis of systems with partial state saturation nonlinearities," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol.43, pp.230-232, Mar. 1996.
  6. D. Liu and A. N. Michel, "Asymptotic stability of systems operating on a closed hypercube," Systems & Control Letters, vol.19, pp.281-285, Oct. 1992.
  7. A. N. Michel, D. Liu, and K. Wang, "Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities," International Journal of Robust and Nonlinear Control, vol.5, pp.505-519, Aug. 1995.
  8. D. Liu and A. N. Michel, "Null controllability of systems with control constraints and state saturation," Systems & Control Letters, vol.20, pp.131-139, Feb. 1993.
  9. D. Liu and A. Molchanov, "Criteria for robust absolute stability of time-varying nonlinear continuous-time systems," Automatica, vol.38, pp.627-637, Apr. 2002.
  10. A. Molchanov and D. Liu, "Robust absolute stability of nonlinear time-varying discrete-time systems," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 49, pp.1129-1137, Aug. 2002.

Derong Liu's Other Publication on Stability Analysis

  1. K. Wang, A. N. Michel, and D. Liu, "Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices," IEEE Transactions on Automatic Control, vol.39, pp.1251-1255, June 1994. corrections.
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Author: Derong Liu               E-Mail: dliu@ece.uic.edu