The Non-uniform in Time Small-Gain Theorem for a Wide Class of Control Systems with Outputs

The notions of non-uniform in time robust global asymptotic output stability and non-uniform in time input-tooutput stability (IOS) are extended to cover a wide class of control systemswith outputs that includes (finite or infinitedimensional) discrete-time and continuous-time control systems. A small-gain theorem,which makes use of the notion of non-uniform in time IOS property,is presented.

[1]  Eduardo Sontag,et al.  Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations , 1999 .

[2]  Eduardo Sontag,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999, at - Automatisierungstechnik.

[3]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

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

[5]  Zhong-Ping Jiang,et al.  Nonlinear small-gain theorems for discrete-time feedback systems and applications , 2004, Autom..

[6]  Iasson Karafyllis,et al.  Non‐uniform in time robust global asymptotic output stability for discrete‐time systems , 2005, Syst. Control. Lett..

[7]  Eduardo Sontag,et al.  Notions of input to output stability , 1999, Systems & Control Letters.

[8]  Eduardo Sontag Comments on integral variants of ISS , 1998 .

[9]  Brian Ingalls,et al.  On Input-to-Output Stability for Systems not Uniformly Bounded , 2001 .

[10]  Iasson Karafyllis,et al.  A Converse Lyapunov Theorem for Nonuniform in Time Global Asymptotic Stability and Its Application to Feedback Stabilization , 2003, SIAM J. Control. Optim..

[11]  Eduardo D. Sontag,et al.  Lyapunov Characterizations of Input to Output Stability , 2000, SIAM J. Control. Optim..

[12]  A. Teel A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[13]  Y. Wang,et al.  A Lyapunov Formulation of Nonlinear Small Gain Theorem for Interconnected Systems , 1995 .

[14]  R. Kálmán Mathematical description of linear dynamical systems , 1963 .

[15]  Yuan Wang,et al.  A local nonlinear small-gain theorem for discrete-time feedback systems , 2000 .

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

[17]  Iasson Karafyllis Necessary and sufficient conditions for the existence of stabilizing feedback for control systems , 2003, IMA J. Math. Control. Inf..

[18]  Zhong-Ping Jiang,et al.  A converse Lyapunov theorem for discrete-time systems with disturbances , 2002, Syst. Control. Lett..

[19]  Zhong-Ping Jiang,et al.  A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems , 1996, Autom..

[20]  Iasson Karafyllis,et al.  Nonuniform in time input-to-state stability and the small-gain theorem , 2004, IEEE Transactions on Automatic Control.

[21]  Zhong-Ping Jiang,et al.  A small-gain control method for nonlinear cascaded systems with dynamic uncertainties , 1997, IEEE Trans. Autom. Control..

[22]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[23]  Eduardo D. Sontag,et al.  A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections , 2002, J. Frankl. Inst..

[24]  Alberto Isidori,et al.  Nonlinear Control Systems II , 1999 .

[25]  Eduardo D. Sontag,et al.  Mathematical control theory: deterministic finite dimensional systems (2nd ed.) , 1998 .

[26]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.