1,082 research outputs found
Further Remarks on Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems
We study the stability properties of a class of time-varying nonlinear
systems. We assume that non-strict input-to-state stable (ISS) Lyapunov
functions for our systems are given and posit a mild persistency of excitation
condition on our given Lyapunov functions which guarantee the existence of
strict ISS Lyapunov functions for our systems. Next, we provide simple direct
constructions of explicit strict ISS Lyapunov functions for our systems by
applying an integral smoothing method. We illustrate our constructions using a
tracking problem for a rotating rigid body.Comment: 6 pages, submitted for publication in June 200
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
Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems
We provide explicit closed form expressions for strict Lyapunov functions for
time-varying discrete time systems. Our Lyapunov functions are expressed in
terms of known nonstrict Lyapunov functions for the dynamics and finite sums of
persistency of excitation parameters. This provides a discrete time analog of
our previous continuous time Lyapunov function constructions. We also construct
explicit strict Lyapunov functions for systems satisfying nonstrict discrete
time analogs of the conditions from Matrosov's Theorem. We use our methods to
build strict Lyapunov functions for time-varying hybrid systems that contain
mixtures of continuous and discrete time evolutions.Comment: 14 pages. Accepted for publication in Nonlinear Analysis: Hybrid
Systems and Applications on September 6, 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
Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach
Lyapunov-Krasowskii functionals are used to design quantized control laws for
nonlinear continuous-time systems in the presence of constant delays in the
input. The quantized control law is implemented via hysteresis to prevent
chattering. Under appropriate conditions, our analysis applies to stabilizable
nonlinear systems for any value of the quantization density. The resulting
quantized feedback is parametrized with respect to the quantization density.
Moreover, the maximal allowable delay tolerated by the system is characterized
as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals,
and System
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
Interval observers for linear time-invariant systems with disturbances
International audienceIt is shown that, for any time-invariant exponentially stable linear system with additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. The approach is applied to detectable linear systems
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
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