1. M. Malisoff, M. Krichman, and E.D. Sontag. Global stabilization for systems evolving on manifolds. Journal of Dynamical and Control Systems, 12:161-184, 2006. [PDF] Keyword(s): nonlinear stability, nonlinear control, feedback stabilization. Abstract:

   This paper shows that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since discontinuous feedbacks are allowed, solutions are understood in the ``sample and hold'' sense introduced by Clarke-Ledyaev-Sontag-Subbotin (CLSS). This work generalizes the CLSS Theorem, which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds relative to actuator errors, under small observation noise.




2. M. Malisoff and E.D. Sontag. Asymptotic controllability and input-to-state stabilization: the effect of actuator errors. In Optimal control, stabilization and nonsmooth analysis, volume 301 of Lecture Notes in Control and Inform. Sci., pages 155-171. Springer, Berlin, 2004. [PDF] Keyword(s): input to state stability, control-Lyapunov functions, nonlinear control, feedback stabilization, ISS. Abstract:

   We discuss several issues related to the stabilizability of nonlinear systems. First, for continuously stabilizable systems, we review constructions of feedbacks that render the system input-to-state stable with respect to actuator errors. Then, we discuss a recent paper which provides a new feedback design that makes globally asymptotically controllable systems input-to-state stable to actuator errors and small observation noise. We illustrate our constructions using the nonholonomic integrator, and discuss a related feedback design for systems with disturbances.




3. M. Malisoff, L. Rifford, and E.D. Sontag. Global Asymptotic Controllability Implies Input-to-State Stabilization. SIAM J. Control Optim., 42(6):2221-2238, 2004. [PDF] [doi:http://dx.doi.org/10.1137/S0363012903422333] Keyword(s): input to state stability, control-Lyapunov functions, nonlinear control, feedback stabilization. Abstract:

   The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for fully nonlinear GAC systems with actuator errors are also discussed. Our controllers have the property that they tolerate small observation noise as well.




4. M. Malisoff and E.D. Sontag. Universal formulas for feedback stabilization with respect to Minkowski balls. Systems Control Lett., 40(4):247-260, 2000. [PDF] Keyword(s): nonlinear control, feedback stabilization, saturation, control-Lyapunov functions, bounded inputs. Abstract:

   This note provides explicit algebraic stabilizing formulas for clf's when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a theorem of Artstein, but the proof of Artstein's theorem is nonconstructive. The formulas are obtained from a general feedback stabilization technique and are used to construct approximation solutions to some stabilization problems.

1. M. Malisoff, L. Rifford, and E.D. Sontag. Remarks on input to state stabilization. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003, pages 1053-1058, 2003. [PDF] Keyword(s): nonlinear control, feedback stabilization.



2. M. Malisoff and E.D. Sontag. Universal formulas for CLF's with respect to Minkowski balls. In Proc. American Control Conf., San Diego, June 1999, pages 3033-3037, 1999.

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