Recent results on Lyapunov-theoretic techniques for nonlinear stability

Establishes a converse Lyapunov function theorem useful for studying stability of systems with disturbances. The result applies to global stability with respect to closed, not necessarily compact, invariant sets, and the resulting Lyapunov functions are smooth.

[1]  J. L. Massera.  Contributions to Stability Theory , 1956 .

[2]  Solomon Lefschetz,et al.  Differential Equations: Geometric Theory , 1958 .

[3]  P. Seibert.  Stability under Perturbations in Generalized Dynamical Systems , 1963 .

[4]  H. Fédérer.  Geometric Measure Theory , 1969 .

[5]  F. Wilson,et al.  Smoothing derivatives of functions and applications , 1969 .

[6]  A. Fuller,et al.  Stability of Motion , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Vimal Singh,et al.  Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  Jean-Pierre Aubin,et al.  Differential Inclusions - Set-Valued Maps and Viability Theory , 1984, Grundlehren der mathematischen Wissenschaften.

[9]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[10]  V. Lakshmikantham,et al.  Stability Analysis of Nonlinear Systems , 1988 .

[11]  John Tsinias.  A Lyapunov description of stability in control systems , 1988 .

[12]  Eduardo D. Sontag.  Some connections between stabilization and factorization , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[13]  Y. Pyatnitskiy,et al.  Criteria of asymptotic stability of differential and difference inclusions encountered in control theory , 1989 .

[14]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[15]  Eduardo Sontag.  Further facts about input to state stabilization , 1990 .

[16]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[17]  Jean-Pierre Aubin,et al.  Viability theory , 1991 .

[18]  John Tsinias,et al.  Versions of Sontag's 'input to state stability condition' and the global stabilizability problem , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[19]  I. Kanellakopoulos,et al.  A toolkit for nonlinear feedback design , 1992 .

[20]  J. Tsinias.  Sontag's “input to state stability condition” and global stabilization using state detection , 1993 .

[21]  L. Praly,et al.  Stabilization by output feedback for systems with ISS inverse dynamics , 1993 .

[22]  Yuandan Lin,et al.  A Smooth Converse Lyapunov Theorem for Robust Stability , 1996 .