Cascade lemma for set-stable systems

A previous result about uniform global asymptotic stability (UGAS) of the equilibrium of a cascaded time-varying systems, is here also shown to hold for closed (not necessarily compact) sets composed by set-stable subsystems of a cascade. In view of this result an optimal control allocation approach is discussed

[1]  Tor Arne Johansen,et al.  Optimizing nonlinear adaptive control allocation , 2006 .

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

[3]  R. Suárez,et al.  Global stabilization of nonlinear cascade systems , 1990 .

[4]  W. Walter Differential and Integral Inequalities , 1970 .

[5]  Antonio Loría,et al.  Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems , 2001, Autom..

[6]  Yuan Wang,et al.  Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability , 1996, Math. Control. Signals Syst..

[7]  P. Kokotovic,et al.  The peaking phenomenon and the global stabilization of nonlinear systems , 1991 .

[8]  Antonio Loría,et al.  Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications , 2002, Math. Control. Signals Syst..

[9]  A. Teel,et al.  A Smooth Lyapunov Function from a Class-kl Estimate Involving Two Positive Semideenite Functions , 1999 .

[10]  Growth Conditions for Global Stabilization of Cascade Nonlinear Systems , 1995 .

[11]  T.A. Johansen,et al.  Adaptive Optimizing Dynamic Control Allocation Algorithm for Yaw Stabilization of an Automotive Vehicle using Brakes , 2006, 2006 14th Mediterranean Conference on Control and Automation.

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

[13]  A. Teel,et al.  A smooth Lyapunov function from a class- ${\mathcal{KL}}$ estimate involving two positive semidefinite functions , 2000 .

[14]  T. Johansen Optimizing nonlinear control allocation , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[16]  M. Vidyasagar Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability , 1980 .

[17]  David J. Hill,et al.  Input-output and input-to-state stabilization of cascaded nonlinear systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[18]  Romeo Ortega,et al.  Passivity properties for stabilization of cascaded nonlinear systems , 1991, Autom..

[19]  Eduardo Sontag Remarks on stabilization and input-to-state stability , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.