Browsing by Subject "Stability analysis"
Now showing 1 - 17 of 17
Results Per Page
Sort Options
Item Open Access Controller design for plants with internal delayed feedback(Institute of Electrical and Electronics Engineers, 2022-05-01) Gündeş, A. N.; Özbay, HitayA special class of retarded and neutral time delay systems is considered. These are plants with internal delayed feedback, and they may have finitely many or infinitely many unstable poles. Stabilizing controllers are obtained from a particular interpolation. A parametrization of all stabilizing integral-action controllers is obtained. Examples are given to illustrate this simple design procedure and its robustness properties for various uncertainties.Item Open Access Essays on gene regulatory network models and their stability analysis(Bilkent University, 2023-07) Şener, Dilan ÖztürkGene expression is one of the core areas in comprehending and assessing how biological cells work. Gene regulatory networks (GRNs), representing the intri-cate mechanism between genes and their regulatory modules, are instrumental in controlling gene expression and cell functions. These models shed light on how transcription factors interact with their regulatory modules within a cell. Despite the multitude of studies focusing on the analysis and enhancement of GRNs, there is still room for contributions. This thesis investigates a novel framework inspired by the gene networks constructed using synthetic biology, and presents stability analyses of the nonlinear infinite dimensional dynamical system models arising in this framework. In the first part of the thesis, we extend a previously studied benchmark GRN model including time delay, and present an analysis of the extended frame-work. We utilize unmodeled dynamics and possibly ignored interactions, including higher-order dynamics, in our system design. The stability of the extended system is analyzed by considering various nonlinearity functions and design pa-rameters, and the results are compared with those of the benchmark original model. In the second part, we employ an extension of a gene network model using a multiplicative perturbation of the dynamical system. Each cascaded subsystem in this extended framework has an additional block, including a multiplicative term with a high-pass filter, and the effect of additional parameters on the robustness and delay margin of the system is investigated. Experiments with various design parameters yield that the stability characteristics of GRNs can be improved using the model pertaining to the extension under specific perturbations. Finally, the third part covers the analysis of nonlinear dynamics and chaos in GRNs, particularly focusing on the two-gene original and extended gene net-works. Chaotic dynamics depend strongly on the inclusion of time delays, but the circuit motifs that show chaos differ when both original and extended models are considered. Our results suggest that for a particular higher-order extension of the gene network, it is possible to observe the chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of the modification of the original benchmark model induced by unmodeled dynamics. We argue that regulatory gene circuit models with additional parameters demonstrate non-periodic dynamics much more easily.Item Open Access On stability of interval matrices(Institute of Electrical and Electronics Engineers, 1994-02) Sezer, M. E.; Siljak, D. D.New sufficient, and sometimes necessary and sufficient conditions, are obtained for Schur- and Hurwitz-stability of interval matrices by relying on the concept of connective stability and M-matrices. The necessity part is broadened to include interval matrices with mixed signs of the off-diagonal elements, provided the sign patterns follow that of the Morishima matrix. The obtained results are extended to cover convex combinations of interval matrices.Item Open Access On the Delay Margin for Consensus in Directed Networks of Anticipatory Agents(Elsevier B.V., 2016) Irofti D.; Atay, F. M.We consider a linear consensus problem involving a time delay that arises from predicting the future states of agents based on their past history. In case the agents are coupled in a connected and undirected network, the exact condition for consensus is that the delay be less than a constant threshold that is independent of the network topology or size. In directed networks, however, the situation is quite different. We show that the allowable maximum delay for consensus depends on the network topology in a nontrivial way. We study this delay margin in several network constellations, including various circulant networks with directed links. We show that the delay margin depends not only on the number of neighbors, but also on the directionality of connections with those neighbors. Furthermore, the delay margin improves as the circulant networks are rewired en route to a small-world configuration. © 2016Item Open Access PID controller design for fractional-order systems with time delays(Elsevier, 2011-11-22) Özbay, Hitay; Bonnet, C.; Fioravanti, A.R.Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of sα, where 0<α<1, and s is the Laplace transform variable. Effect of inputoutput time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants.Item 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.Item 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.Item Open Access Stability analysis of human–adaptive controller interactions(American Institute of Aeronautics and Astronautics (AIAA), 2017) Yücelen, T.; Yıldız, Yıldıray; Sipahi, R.; Yousefi, Ehsan; Nguyen, N.In this paper, stability of human in the loop model reference adaptive control architectures is analyzed. For a general class of linear human models with time-delay, a fundamental stability limit of these architectures is established, which depends on the parameters of this human model as well as the reference model parameters of the adaptive controller. It is shown that when the given set of human model and reference model parameters satisfy this stability limit, the closed-loop system trajectories are guaranteed to be stable. © 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Item Open Access Stability analysis of switched systems using Lyapunov-Krasovskii functionals(Elsevier, 2011) Çalişkan, S.Y.; Özbay, Hitay; Niculescu, S.-I.Piecewise Lyapunov-Razumikhin functions are previously used for obtaining a lower bound for the dwell time of the switched time delay systems under the assumption that each candidate system is delay dependently stable. In this work, using Lyapunov-Krasovskii functionals, a less conservative lower bound for the dwell time is obtained. Improvement in the dwell time is illustrated with an example. © 2011 IFAC.Item Open Access Stability analysis of switched systems with time-varying discontinuous delays(IEEE, 2017) Mazenc, F.; Malisoff, M.; Özbay, HitayA 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.Item Open Access Stability analysis of switched time-delay systems(IEEE, 2008-12) Yan, P.; Özbay, HitayThis 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.Item Open Access Stability analysis of systems with distributed delays and application to hematopoietic cell maturation dynamics(IEEE, 2008-12) Özbay, Hitay; Bonnet, C.; Clairambault, J.We consider linear systems with distributed delays where delay kernels are assumed to be finite duration impulse responses of finite dimensional systems. We show that stability analysis for this class of systems can be reduced to stability analysis of linear systems with discrete delays, for which many algorithms are available in the literature. The results are illustrated on a mathematical model of hematopoietic cell maturation dynamics. © 2008 IEEE.Item Open Access Stability analysis of the heat equation with time-delayed feedback(IFAC, 2009-06) Çalışkan, Sina Yamaç; Özbay, HitayIn this paper we consider the heat equation with time delayed feedback. Recently, stability analysis of this system, with possibly time-varying delay, is done by Fridman and Orlov (2007, 2009); and a sufficient condition is obtained for stability in terms of a linear matrix inequality. Here we consider the same system, but with constant delay, and perform the stability analysis in the frequency domain. A necessary and sufficient condition is obtained in terms of the system parameters. The result is illustrated with numerical examples. © 2009 IFAC.Item Open Access Stability of delayed feedback controllers for discrete time systems(IEEE, 2003) Morgül, ÖmerWe consider the delayed feedback control (DFC) scheme for one dimensional discrete time systems. To analyze the stability, we construct a map whose fixed points correspond to the periodic orbits of the system to be controlled. Then the stability of the DFC is equivalent to the stability of the corresponding equilibrium point of the constructed map.Item Open Access Stability of planar piecewise linear systems :a geometric approach(Bilkent University, 2015-09) Abdullahi, AdamuThis thesis focuses on the stability analysis of piecewise linear systems. Such systems consist of linear subsystems, each of which is active in a particular region of the state-space. Many practical and theoretical systems can be modelled as piecewise linear systems. Despite their simple structure, analysis of piecewise linear systems can be rather complex. For instance, most of the results for stability can be based on a Lyapunov approach. However, a major drawback of applying this method is that, it usually only provides su cient conditions for stability. A geometric approach will be used to derive new stability criteria for planar piecewise linear systems. Any planar piecewise linear (multi-modal) system is shown to be globally asymptotically stable just in case each linear mode satis es certain conditions that solely depend on how its eigenvectors stand relative to the cone on which it is de ned. The stability conditions are in terms of the eigenvalues, eigenvectors, and the cone. The improvements on the known stability conditions are the following: i) The condition is directly in terms of the \givens" of the problem. ii) Non-transitive modes are identi ed. iii) Initial states and their trajectories are classi ed (basins of attraction and repulsion are indicated). iv) The known condition for bimodal systems is obtained as an easy corollary of the main result. Additionally, using our result on stability, we design a hybrid controller for a class of second order LTI systems that do not admit a static output feedback controller. The e ectiveness of the proposed controller is illustrated on a magnetic levitation system.Item Open Access Stability of third order conewise linear systems(Bilkent University, 2019-07) Zakwan, MuhammadA conewise linear, time-invariant system is a piecewise linear system in which the state-space is a union of polyhedral cones. Each cone has its own dynamics so that a multi-modal system results. We focus our attention to global asymptotic stability so that each mode (or subsystem) is autonomous. i.e., driven only by initial states. Conewise linear systems are of great relevance from both practical and theoretical point of views as they represent an immediate extension of linear, time-invariant systems. A clean and complete necessary and sufficient condition for stability of this class of systems has been obtained only when the cones are planar, that is only when the state space is R2. This thesis is devoted to the case of state-space being R3, although occasionally we also consider the general case Rn. We aim to determine conditions for stability exploring the geometry of the modes. Thus our results do not make use of a Lyapunov function based approach for stability analysis. We first consider an individual mode and determine whether a cone with a given dynamics can be classified as a sink, source, or transitive from one or two borders. It turns out that the classification not only depends on the geometry of the eigenvectors and the geometry of the cone but also on entries of the A-matrix that defines the dynamics. Under suitable assumptions on the configuration of the eigenvectors relative to the cone, we manage to obtain relatively clean charecterizations for transitive modes. Combining this with a complete characterization of sinks and sources, we use some tools from graph theory and obtain an interesting sufficient condition for stability of a conewise system composed of transitive modes, sources, and sinks. Finally, we apply our results to study the stability of a linear RC electrical network containing diodes.Item Open Access Switched PD-like controllers for first order unstable systems with time delay(IFAC, 2009) Arslan, Gül Ezgi; Özbay, HitayA new method is proposed for the design of PD-like (first order stable) controllers for switched first order unstable systems with time delays. For this purpose, a dwell-time based stability condition of Yan and Özbay (2008) is used for the class of switched time delay systems studied here. The proposed method finds the values of PD-like controller parameters which minimize an upper bound of the dwell time, minimum time needed between the switching instants to preserve stability. The conservatism analysis of this method is done by time domain simulations. The results show that the calculated upper bound for the dwell time is close to the lower bound of the dwell time observed by simulations.