... STABILIZATION AND CONTROLOF UNSTABLE TIMEDELAYSYSTEMS LEE SEE CHEK (B.Eng (Hons., 1st Class) UTM, M.Sc NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL ... unstable timedelay process can be stabilized or not, depends on the timedelay magnitude When the normalized timedelay exceeds 2, a PID controller has no stabilization solution In this thesis, a controller ... stabilizability condition by P and PI controllers, on the other hand, is to be proven independently The same is true for PD and PID controllers 2.3 P/PI controller The stabilizationby P or PI controller will...
... h∞ controlof linear time- delaysystems IEEE Trans Aut Control 47(2), 253– 270 Fridman, E and U Shaked (2002b) An improved stabilization method for linear time- delaysystems IEEE Trans Aut Control ... (2004) Delaydependent robust h∞ control for uncertainsystems with a state -delay Automatica 40, 65–72 Li, X and C.E De Souza (1997) Delay -dependent robust stability and stabilizationofuncertain ... on the stability of time- delaysystems In: ROCOND Toulouse Submitted Gu, K (1997) Discretized LMI set in the stability problem of linear uncertain time- delaysystems Internat J Control 68, 923–934...
... exponential stabilizability of discrete -time systems with time- delayed states Finally, as an application, we consider the global stabilizationof the nonlinear controlsystems Preliminaries In this ... feedback stabilizability of perturbed controlsystems with both time- varying and timedelayed states Our main contributions are as follows By applying the “freezing” technique to the control system 1.1 ... for discrete -time systems, ” IEEE e Transactions on Automatic Control, vol 41, no 6, pp 903–907, 1996 12 E N Chukwu, Stability and Time- Optimal Controlof Hereditary Systems, vol 188 of Mathematics...
... available as in the un-delayed case Consequently, the problem of the finite -time controlof linear time- delaysystems with bounded controls is of interest in its own right Motivated by the above discussions, ... Perruquetti W (2008), Finite -time stability and stabilizationof time- delaysystems Syst Contr Lett., 57, 561-566 [15] Gu K., Kharitonov V.L & Chen J (2003), Stability ofTimeDelaySystems Boston, Birkhauser ... stabilizationof linear systems Automatica, 46, 1558-1562 [3] Liu H., Shena Y & Zhao X (2012), Delay -dependent observer-based H∞ finite -time control for switched systems with time- varying delay Nonl...
... Applications to Control Theory 92 5.6 Stability of Time- DelaySystems with a Single Delay 99 5.7 Notes and References 106 Stabilizationof Time- DelaySystems using a Constant Gain Feedback Controller ... Proof of Lemmas 8.3, 8.4, and 8.5 A.l Preliminary Results A.2 Proof of Lemma 8.3 A.3 Proof of Lemma 8.4 A.4 Proof of Lemma 8.5 297 297 301 302 303 B Proof of Lemmas 8.7 and 8.9 B.l Proof of Lemma ... and is (1) independentof the particular values of the constant disturbances or references, (2) independentof the initial conditions of the plant and controller, and (3) independentof whether...
... analysis ofstabilizationof a class of linear time invariant systems with timedelay Section contains an overview of the representation of entire functions as an infinite product by way of Weierstrass’ ... with timedelay The problem of stability of linear time invariant systems with timedelay make necessary a method for localization of the roots of analytic functions These systems are described by ... Tracking Controlof Input Delayed Robotic Manipulators Haiping Du and Weihua Li 211 Preface The problem of investigation oftimedelaysystems has been explored over many years Timedelay is very often...
... S.P (2000) StabilizationofTimeDelaySystems Proceedings of the American Control Conference, pp 963–970, Chicago Silva, G J., Datta, A & Bhattacharyya, S.P (2001) Determination of Stabilizing ... possible the construction of Lyapunov stability theory even for the timedelaysystems in that sense that asymptotic 28 Time- DelaySystems stability is equivalent to the existence of symmetric, positive ... Synthesis of PID Controllers for a Class ofTimeDelaySystems Automatica, Vol 45, Issue 7, July 2009, pp 1778-1782, ISSN 0024-3795 Özgüler, A B and Koçan, A A (1994) An analytic determination of stabilizing...
... study of such systems, there are still many problems to be considered Timedelaysystems 2.1 Continuous timedelaysystems 2.1.1 Continuous timedelaysystems – stability in the sense of Lyapunov ... of Mechanical Engineering, 2Ruhr-University of Bochum, 1Serbia 2Germany Introduction The problem of investigation oftimedelaysystems has been exploited over many years Timedelay is very often ... previous proof of Theorem 2.1.2.9 Q.E.D 2.2 Discrete timedelaysystems 2.2.1 Discrete timedelaysystems – stability in the sense of Lyapunov ASYMPTOTIC STABILITY-APPROACH BASED ON THE RESULTS OF TISSIR...
... stability of singular and descriptive timedelay systems, which are considered in detail in this section 3.1 Continuous singular time delayed systems 3.1.1 Continuous singular time delayed systems ... treating the problem of finite time stability for discrete descriptor timedelaysystems Only one paper has been written in 62 Time- DelaySystems context of practical and finite time stability for ... stabilty of particular class of continual and discrete timedelaysystems on finite and infinite time interval, Diploma Work, School of Mechanical Eng., University of Belgrade, Department of Control...
... V Simeunovic, (2011.b) On nonLyapunov delay -independent and delay -dependent criteria for particular class of 72 Time- DelaySystems continuous timedelay systems, Proc CDC, December 3-5, Orlando ... the Stability of Time- DelaySystems in the Sense of Non-Lyapunov Delay -Independent and Delay -Dependent Criteria, Proc SISY 2010 (IEEE 8th International Symposium on Intelligent Systems and Informatics), ... of linear systems with single time delay, Systems & Control Letters (23), pp 375 – 379, ISSN: 0167-6911 Su, J H & C G Huang, (1992) Robust stability ofdelay dependence for linear uncertain systems, ...
... for uncertain switched systems with time delay, Nonlinear Analysis:Hybrid systems, 2, 81-95 Niamsup, P (2008) Controllability approach to H∞ control problem of linear time- varying switched systems, ... (2004) Delay -dependent criteria for robust stability oftime varying delay systems, Automatica J IFAC, 40, 1435-1439 Xie, G & Wang, L (2006) Quadratic stability and stabilizationof discrete time ... switched systems with time delay, Nonlinear Analysis:Hybrid systems, 2, 913-921 Boyd, S et al (1994) Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia 96 Time- Delay Systems...
... types of chemical reactors Plants with a timedelay often cannot be controlled by usual controllers designed without consideration of the dead -time There are various ways to control such systems ... with timedelay Int J Control, 58, pp 1025-1036 126 Time- DelaySystems Dostál, P., Bobál, V., and Prokop, R (2001) Design of simple controllers for unstable timedelaysystems using LQ control ... plant types of integrating and unstable timedelay systems: an integrating timedelay system (ITDS), an unstable first order timedelay system (UFOTDS), an unstable second order timedelay system...
... In all of the papers discussed above, the authors investigated delay -independent stabilization and controlof time- delaysystemsDelay -dependent stabilization and H∞ controlof time- delaysystems ... focused on the stabilizationof the class of time- delaysystems with parametric uncertainties and time varying state delay when the states are not assumed to be measurable For this class of systems, ... Nounou (2006) to consider designing delay -dependent adaptive controllers for a class ofuncertain time- delaysystems with time- varying delays in the presence of nonlinear perturbation In Nounou...
... a class of continuous time- delay systems, IMA Journal of Mathematical Control and Information 23: 225–235 Nounou, H N (2006) Delaydependent adaptive controlofuncertain time- delay systems, ... Adaptive ControlofUncertain Time- DelaySystems 159 Choi, H (2001) Variablestructurecontrolof dynamical systems with mismatched norm-bounded uncertainties: An lmi approach, Int J Control 74(13): ... Adaptive ControlofUncertain Time- DelaySystems ˆ β3 < − γ, and ρ(0) > 1, then the control law (3) will guarantee asymptotic stabilizationof the closed-loop system Proof The time derivative of Vb...
... Delay -independent sliding mode controlof nonlinear time- delay systems, ” American Control Conference, pp 4068-4073, 2005 [9] Y Xia and Y Jia, “Robust sliding-mode control for uncertain time- delay ... S(t ) Fig Control effort u(t ) 175 176 Time- DelaySystems Conclusion In this paper, the robust control problem of a class ofuncertain nonlinear time- delaysystems has been solved by the proposed ... synthesis of nonlinear time- delaysystems via fuzzy control approach,” IEEE Trans Fuzzy Systems, vol.8, no.2, pp 200-210, 2000 Sliding Mode Control for a Class of Multiple Time- DelaySystems 177...
... in Synchronization of Multiple TimeDelaySystems 207 value of parameters and delays Recall that, in the specific example of single time- delay Mackey-Glass system examined by J.D Farmer (Farmer, ... Synchronization of Multiple TimeDelaySystems (arb units) (arb units) (a) Time series of x ( t) and y( t) (b) Portrait of x ( t + 4.6) versus y( t) Fig 11 Simulation result of projective-anticipating ... synchronization manifold of −2.5y(t) = 1.5x (t + 4.6) It is easy to observed the scale factor by means of the scale of vertical axes in 202 (arb units) (arb units) (arb units) Time- DelaySystems (arb units)...
... 2009), and the issue oftimedelay for robotic systems has been studied through the passivity property For systems with time delays, both delaydependent and delayindependentcontrol strategies ... of view, one of the current focus on the controloftimedelaysystems is to develop less conservative approaches so that the controller can stabilise the systems or can achieve the defined control ... scope of this chapter, and will not be further discussed 224 Time- DelaySystems 1.5 1.5 Actual state variable Reference state variable Actual state variable Reference state variable 0.5 State variable...
... the delay incorporated by each of the nodes is inversely proportional to the remaining energy level of each of the corresponding nodes The delay is calculated as d=D− D∗ e , E (1) where d is a delay ... End-to-end delay is the time between the reception of the last and first packet/total number of packets reaching the application layer (iii) Control overhead is measured as the total number ofcontrol ... the design and implementation of energy-based timedelay routing (EBTDR) algorithm in the existing DSR protocol by introducing a delay in forwarding the packets by nodes, which is inversely proportional...
... analysis ofstabilizationof a class of linear time invariant systems with timedelay Section contains an overview of the representation of entire functions as an infinite product by way of Weierstrass’ ... with timedelay The problem of stability of linear time invariant systems with timedelay make necessary a method for localization of the roots of analytic functions These systems are described by ... study of such systems, there are still many problems to be considered Timedelaysystems 2.1 Continuous timedelaysystems 2.1.1 Continuous timedelaysystems – stability in the sense of Lyapunov...
... Laplace transform of the solutions of the timedelay system The note is organized as follows After some preliminaries on delaysystems in the next section we describe the construction of the Lyapunov-Krasovskii ... approach to the robust stability analysis of time- delaysystems Automatica, 39:15–20, 2003 [10] V L Kharitonov and E Plischke Lyapunov matrices for time- delaysystems Report ???, Zentrum f¨ r Technomathematik, ... Krasovski˘ On the application of the second method of Lyapunov for equations ı with time delays Prikl Mat Meh., 20:315–327, 1956 [12] B S Razumikhin On stability ofsystems with a delay Prikl Mat Meh.,...