Displaying similar documents to “Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems”

Smooth homogeneous asymptotically stabilizing feedback controls

H. Hermes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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If a smooth nonlinear affine control system has a controllable linear approximation, a standard technique for constructing a smooth (linear) asymptotically stabilizing feedbackcontrol is via the LQR (linear, quadratic, regulator) method. The nonlinear system may not have a controllable linear approximation, but instead may be shown to be small (or large) time locally controllable via a high order, homogeneous approximation. In this case one can attempt to construct an asymptotically...

On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients

Ludovic Rifford (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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Let x ˙ = f ( x , u ) be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...

Constrained stabilization of a dynamic systems: a case study

Franco Blanchini, S. Cotterli, G. Koruza, S. Miani, R. Siagri, Luciano Tubaro (1999)

Kybernetika

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In this work we consider the problem of determining and implementing a state feedback stabilizing control law for a laboratory two-tank dynamic system in the presence of state and control constraints. We do this by exploiting the properties of the polyhedral Lyapunov functions, i. e. Lyapunov functions whose level surfaces are polyhedra, in view of their capability of providing an arbitrarily good approximation of the maximal set of attraction, which is the largest set of initial states...