115 research outputs found
Further Constructions of Control-Lyapunov Functions and Stabilizing Feedbacks for Systems Satisfying the Jurdjevic-Quinn Conditions
For a broad class of nonlinear systems, we construct smooth control-Lyapunov
functions whose derivatives along the trajectories of the systems can be made
negative definite by smooth control laws that are arbitrarily small in norm. We
assume our systems satisfy appropriate generalizations of the Jurdjevic-Quinn
conditions. We also design state feedbacks of arbitrarily small norm that
render our systems integral-input-to-state stable to actuator errors.Comment: 15 pages, 0 figures, accepted for publication in IEEE Transactions on
Automatic Control in October 200
Further Results on Lyapunov Functions for Slowly Time-Varying Systems
We provide general methods for explicitly constructing strict Lyapunov
functions for fully nonlinear slowly time-varying systems. Our results apply to
cases where the given dynamics and corresponding frozen dynamics are not
necessarily exponentially stable. This complements our previous Lyapunov
function constructions for rapidly time-varying dynamics. We also explicitly
construct input-to-state stable Lyapunov functions for slowly time-varying
control systems. We illustrate our findings by constructing explicit Lyapunov
functions for a pendulum model, an example from identification theory, and a
perturbed friction model.Comment: Accepted for publication in Mathematics of Control, Signals, and
Systems (MCSS) on November 20, 200
Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems
We explicitly construct global strict Lyapunov functions for rapidly
time-varying nonlinear control systems. The Lyapunov functions we construct are
expressed in terms of oftentimes more readily available Lyapunov functions for
the limiting dynamics which we assume are uniformly globally asymptotically
stable. This leads to new sufficient conditions for uniform global exponential,
uniform global asymptotic, and input-to-state stability of fast time-varying
dynamics. We also construct strict Lyapunov functions for our systems using a
strictification approach. We illustrate our results using a friction control
example.Comment: 10 pages, 0 figues, revised and accepted for publication as a regular
paper in Automatica in May 2006. To appear in October 2006 issu
Reduction Model Approach for Systems with a Time-Varying Delay
International audienceWe provide a reduction model approach for achieving global exponential stabilization of linear systems with a time-varying pointwise delay in the input. We allow the delay to be discontinuous and uncertain. We also provide a stability result based on a different dynamic extension that ensures input-to-state stability with respect to additive uncertainties on the dynamics. Instead of the usual Lyapunov-Krasovskii or Razumikhin methods, we use a trajectory based approach
New Control Design for Bounded Backstepping under Input Delays
International audienceWe provide a new backstepping result for time-varying systems with input delays. The novelty of our work is in the bounds on the controls, and the facts that (i) one does not need to compute any Lie derivatives to apply our controls, (ii) the controls have no distributed terms, and (iii) we do not require any differentiability conditions on the available controls for the subsystems
On average values of time-varying delays and a new representation of systems with time-varying delays
We show by a counterexample that the asymptotic stability of a system with a pointwise periodic time-varying delay cannot be deduced from the average value of the delay. We use this counterexample to motivate our new representation of systems with time-varying delays, which we use to develop a new state feedback stabilization method
Further Results on Active Magnetic Bearing Control with Input Saturation
We study the low-bias stabilization of active magnetic bearings (AMBs)
subject to voltage saturation based on a recently proposed model for the AMB
switching mode of operation. Using a forwarding-like approach, we construct a
stabilizing controller of arbitrarily small amplitude and a control-Lyapunov
function for the AMB dynamics. We illustrate our construction using a numerical
example.Comment: 9 pages, 2 figures. IEEE Transactions on Control Systems Technology,
accepted for publication in January 200
STRICT LYAPUNOV FUNCTIONS AND FEEDBACK CONTROLS FOR SIR MODELS WITH QUARANTINE AND VACCINATION
We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals
Continuous-discrete observers for time-varying nonlinear systems: A tutorial on recent results
Continuous-discrete systems can occur when the plant state evolves in continuous time but the output values are only available at discrete instants. Continuous-discrete observers have the valuable property that the observation error between the true state of the system and the observer state converges to zero in a uniform way. The design of continuous-discrete observers can often be done by building framers, which provide componentwise upper and lower bounds for the plant state. This paper is a tutorial on these approaches, highlighting recent results in the literature, and also providing previously unpublished, original results which are not being simultaneously submitted elsewhere
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