On ISS and iISS properties of homogeneous systems

Several conditions are proposed to check input-to-state stability (ISS) and integral input-to-state stability (iISS) properties for generic nonlinear systems applying the weighted homogeneity concept (global or local). The advantages of this result is that, under some mild conditions, the system robustness can be established as a function of the degree of homogeneity.

[1]  A.R. Teel,et al.  On hybrid controllers that induce input-to-state stability with respect to measurement noise , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  Zhong-Ping Jiang,et al.  Robust control of uncertain nonlinear systems via measurement feedback , 1999, IEEE Trans. Autom. Control..

[3]  P. S. Bauer Dissipative Dynamical Systems: I. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Jan C. Willems,et al.  Dissipative Dynamical Systems , 2007, Eur. J. Control.

[5]  L. Rosier Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[6]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[7]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[8]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[9]  E. Ryan Universal stabilization of a class of nonlinear systems with homogeneous vector fields , 1995 .

[10]  Eduardo D. Sontag,et al.  The ISS philosophy as a unifying framework for stability-like behavior , 2001 .

[11]  M. Kawski Nilpotent Lie algebras of vectorfields. , 1988 .

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

[13]  L. Grüne Homogeneous state feedback stabilization of homogeneous systems , 2000, CDC.

[14]  Frank Allgöwer,et al.  Certainty-Equivalence Feedback Design With Polynomial-Type Feedbacks Which Guarantee ISS , 2007, IEEE Transactions on Automatic Control.

[15]  Lars Grüne,et al.  Homogeneous State Feedback Stabilization of Homogenous Systems , 2000, SIAM J. Control. Optim..

[16]  H. Hermes Nilpotent approximations of control systems and distributions , 1986 .

[17]  Denis V. Efimov,et al.  Finite-time output stabilization of the double integrator , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[18]  A. Schaft L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[19]  Eduardo D. Sontag,et al.  Input to state stability and allied system properties , 2011 .

[20]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[21]  Mathukumalli Vidyasagar,et al.  Input-Output Analysis of Large-Scale Interconnected Systems , 1981 .

[22]  Otto J. M. Smith,et al.  Feedback control systems , 1958 .

[23]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[24]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[25]  W. Perruquetti,et al.  Oscillations Conditions in Homogenous Systems , 2010 .

[26]  R. Freeman Global internal stabilizability does not imply global external stabilizability for small sensor disturbances , 1995, IEEE Trans. Autom. Control..

[27]  H. Hermes Homogeneous feedback controls for homogeneous systems , 1995 .

[28]  Yiguang Hong,et al.  Hinfinity control, stabilization, and input-output stability of nonlinear systems with homogeneous properties , 2001, Autom..