Browsing by Subject "Asymptotic stability"

Now showing 1 - 15 of 15

Open Access
Local asymptotic stability conditions for the positive equilibrium of a system modeling cell dynamics in leukemia
(Springer, Berlin, Heidelberg, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun H.; Clairambault J.
A distributed delay system with static nonlinearity has been considered in the literature to study the cell dynamics in leukemia. In this chapter local asymptotic stability conditions are derived for the positive equilibrium point of this nonlinear system. The stability conditions are expressed in terms of inequalities involving parameters of the system. These inequality conditions give guidelines for development of therapeutic actions. © 2012 Springer-Verlag GmbH Berlin Heidelberg.
Open Access
On switching H∞ controllers for a class of linear parameter varying systems
(Elsevier BV, 2007) Yan, P.; Özbay, Hitay
We consider switching H∞ controllers for a class of linear parameter varying (LPV) systems scheduled along a measurable parameter trajectory. The candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable. We provide sufficient conditions to guarantee the stability of the switching LPV systems in terms of the dwell time and the average dwell time. Our results are illustrated with an example, where switching between two robust controllers is performed for an LPV system.
Open Access
On the boundary control of a flexible robot arm
(IEEE, 2001) Morgül, Ömer
We consider a flexible robot arm modeled as a single flexible link clamped to a rigid body. We assume that the system performs only planar motion. For this system, we pose two control problems; namely, the orientation and stabilization of the system. We propose a class of controllers to solve these problems.
Open Access
On the boundary control of Kirchhoff's nonlinear string
(IFAC, 2007) Morgül, Ömer; Shahruz, S. M.
In this paper we propose two new classes of controllers which stabilize Kirchhoff's nonlinear string by using boundary control techniques. We assume that the boundary displacement is the only available measurement. The classes of controllers proposed in this paper are related to the positive real controllers. One of the classes generalizes a special class of such stabilizing controllers which is already proposed in the literature and the other one is new.
Open Access
On the design of dynamic associative neural memories
(IEEE, 1994) Savran, M. E.; Morgül, Ö.
We consider the design problem for a class of discrete-time and continuous-time neural networks. We obtain a characterization of all connection weights that store a given set of vectors into the network; that is, each given vector becomes an equilibrium point of the network. We also give sufficient conditions that guarantee the asymptotic stability of these equilibrium points.
Open Access
On the stabilization of a flexible beam with a tip mass
(Society for Industrial and Applied Mathematics, 1998-11) Conrad, F.; Morgül, Ö.
We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case.
Open Access
Stability analysis of a dynamical model representing gene regulatory networks
(2012) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. I.
In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function. © 2012 IFAC.
Open Access
Stability analysis of cell dynamics in leukemia
(E D P Sciences, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun, H.; Clairambault, J.
In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.
Open Access
Stability analysis of switched systems with time-varying discontinuous delays
(IEEE, 2017) Mazenc, F.; Malisoff, M.; Özbay, Hitay
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.
Open Access
Stability analysis of switched time-delay systems
(IEEE, 2008-12) Yan, P.; Özbay, Hitay
This paper addresses the asymptotic stability of switched time delay systems with heterogenous time invariant time delays. Piecewise Lyapunov-Razumikhin functions are introduced for the switching candidate systems to investigate the stability in the presence of infinite number of switchings. We provide sufficient conditions in terms of the minimum dwell time to guarantee asymptotic stability under the assumptions that each switching candidate is delay-independently or delaydependently stable. Conservatism analysis is also provided by comparing with the dwell time conditions for switched delay free systems. © 2008 IEEE.
Open Access
Stability and robustness analysis for switched systems with time-varying delays
(Society for Industrial and Applied Mathematics Publications, 2018) Mazenc, F.; Malisoff, M.; Özbay, Hitay
A new technique is presented for the stability and robustness analysis of nonlinear switched time-varying systems with uncertainties and time-varying delays. The delays are allowed to be discontinuous (but are required to be piecewise continuous) and arbitrarily long with known upper bounds. The technique uses an adaptation of Halanay’s inequality and a trajectory-based technique, and is used for designing switched controllers to stabilize linear time-varying systems with time-varying delays.
Open Access
Stability of phase difference trajectories of networks of kuramoto oscillators with time-varying couplings and intrinsic frequencies
(Society for Industrial and Applied Mathematics Publications, 2018) Lu, W.; Atay, Fatihcan M.
We study dynamics of phase differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In the case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable if there exists T > 0 such that the aggregation of the time-varying graphs across any time interval of length T has a spanning tree. We also consider the situation that the coupling coefficients may be negative and provide sufficient conditions for the asymptotic stability of the PD dynamics. Due to time variations, the PDs are asymptotic to time-varying patterns rather than constant values. Hence, the PD dynamics can be regarded as a generalization of the well-known phase-locking phenomena. We explicitly investigate several particular cases of time-varying graph structures, including asymptotically periodic PDs due to periodic coupling coefficients and intrinsic frequencies, small perturbations, and fast-switching near constant coupling and frequencies, which lead to PD dynamics close to a phase-locked one. Numerical examples are provided to illustrate the theoretical results.
Open Access
Stabilization and disturbance rejection for the beam equation
(IEEE, 2001) Morgül, Ö.
We consider a system described by the Euler-Bernoulli beam equation. For stabilization, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the controller is a marginally stable positive real function which may contain poles on the imaginary axis. We then give various asymptotical and exponential stability results. We also consider the disturbance rejection problem.
Open Access
Stabilization and disturbance rejection for the wave equation
(Institute of Electrical and Electronics Engineers, 1998-01) Morgül, Ö.
We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function of the complex variable s and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis, provided that the residues corresponding to these poles are nonnegative; the rest of the transfer function is required to be a strictly positive real function. We then show that depending on the location of the pole on the imaginary axis, the closed-loop system is asymptotically stable. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately. We also present some numerical simulation results which support this argument.
Open Access
Three management policies for a resource with partition constraints
(Cambridge University Press, 1999) Alanyalı, M.
Management of a bufferless resource is considered under non-homogeneous demand consisting of one-unit and two-unit requests. Two-unit requests can be served only by a given partition of the resource. Three simple admission policies are evaluated with regard to revenue generation. One policy involves no admission control and two policies involve trunk reservation. A limiting regime in which demand and capacity increase in proportion is considered. It is shown that each policy is asymptotically optimal for a certain range of parameters. Limiting dynamical behavior is obtained via a theory developed by Hunt and Kurtz. The results also point out the remarkable effect of partition constraints.