Finite-time stabilization of uncertain nonlinear planar systems

A stabilizer is described that renders 0 ∈ℝ2 a global finite-time attractor for a class of nonlinear uncertain two-dimensional dynamical systems. The stabilizer is of discontinuous feedback form: the analytic framework is that of differential inclusions. An adaptive version of the stabilizer is also developed that, for a larger class of systems, guarantees global asymptotic attractivity of the origin.

[1]  J. P. Lasalle.  Stability theory for ordinary differential equations. , 1968 .

[2]  J. P. Lasalle.  The stability of dynamical systems , 1976 .

[3]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[4]  E. P. Ryan,et al.  Optimal Relay and Saturating Control System Synthesis , 1982 .

[5]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[6]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .

[7]  J. Willems,et al.  Global adaptive stabilization in the absence of information on the sign of the high frequency gain , 1984 .

[8]  C. Byrnes,et al.  Adaptive stabilization of multivariable linear systems , 1984, The 23rd IEEE Conference on Decision and Control.

[9]  A. S. Morse,et al.  A Three-Dimensional Universal Controller for the Adaptive Stabilization of Any Strictly Proper Minimum-Phase System with Relative Degree Not Exceeding Two , 1985 .

[10]  A. S. Morse,et al.  Correction to "A three-dimensional universal controller for the adaptive stabilization of any strictly proper minimum-phase system with relative degree not exceeding two" , 1985 .

[11]  Bengt Mårtensson,et al.  The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization , 1985 .

[12]  David H. Owens,et al.  High-gain robust adaptive controllers for multivariable systems , 1987 .

[13]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[14]  E. P. Ryan,et al.  Discontinuous Feedback and Universal Adaptive Stabilization , 1990 .

[15]  George Leitmann,et al.  Deterministic control of uncertain systems via a constructive use of Lyapunov stability theory , 1990 .