144 research outputs found
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. © 2006 IEEE
State feedback stabilization of switched systems with delay: Trajectory based approach
We present a new trajectory based approach for state feedback stabilization of switched linear continuous-time systems with a time-varying input delay. In contrast with finding classical common Lyapunov function or multiple Lyapunov functions for establishing the stability of the closed-loop switched system, the new trajectory based approach relies on verifying certain inequalities along the solution of a supplementary system. This study does not make any assumption regarding the stabilizability of all of the constituent subsystems of the switched system. Moreover, no assumption is needed about the differentiability of the delay and no constraint is imposed on the upper bound of the delay derivative. Finally, an illustrative example is included to illustrate the applicability of our results. © 2017 American Automatic Control Council (AACC)
Stability analysis of switched systems with time-varying discontinuous delays
A new technique is proposed to ensure global asymptotic stability for nonlinear switched time-varying systems with time-varying discontinuous delays. It uses an adaptation of Halanay's inequality to switched systems and a recent trajectory based technique. The result is applied to a family of linear time-varying systems with time-varying delays. © 2017 American Automatic Control Council (AACC)
Analysis of Blood Cell Production under Growth Factors Switching
Hematopoiesis is a highly complicated biological phenomenon. Improving its mathematical modeling and analysis are essential steps towards consolidating the common knowledge about mechanisms behind blood cells production. On the other hand, trying to deepen the mathematical modeling of this process has a cost and may be highly demanding in terms of mathematical analysis. In this paper, we propose to describe hematopoiesis under growth factor-dependent parameters as a switching system. Thus, we consider that different biological functions involved in hematopoiesis, including aging velocities, are controlled through multiple growth factors. Then we attempt a new approach in the framework of time-delay switching systems, in order to interpret the behavior of the system around its possible positive steady states. We start here with the study of a specific case in which switching is assumed to result from drug infusions. In a broader context, we expect that interpreting cell dynamics using switching systems leads to a good compromise between complexity of realistic models and their mathematical analysis. © 201
Input-to-state stability of infinite-dimensional control systems
We develop tools for investigation of input-to-state stability (ISS) of
infinite-dimensional control systems. We show that for certain classes of
admissible inputs the existence of an ISS-Lyapunov function implies the
input-to-state stability of a system. Then for the case of systems described by
abstract equations in Banach spaces we develop two methods of construction of
local and global ISS-Lyapunov functions. We prove a linearization principle
that allows a construction of a local ISS-Lyapunov function for a system which
linear approximation is ISS. In order to study interconnections of nonlinear
infinite-dimensional systems, we generalize the small-gain theorem to the case
of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov
function for an entire interconnection, if ISS-Lyapunov functions for
subsystems are known and the small-gain condition is satisfied. We illustrate
the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page
Calculation of transient electromagnetic forces in an axisymmetrical electromagnet with conductive solid parts
The paper describes the analysis and the calculation of transient response of a voltage fed electromagnet. This calculation is based on the simultaneous solution of the magnetic field equations and the electrical circuit equations. In the modelling of the magnetic fields, eddy currents in solid conductive parts and saturation of magnetic parts are taken into account. This modelling uses Finite Element Method for the calculation of magnetic fields and forces with special quadrilateral elements. Experimental and simulation results for an axisymmetrical electromagnet are presented and compared
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