Nonlinear Time Delay Systems

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Author Index
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Extension of Control Lyapunov Functions to Time-Delay Systems

Authors:

Mrdjan Jankovic,

Volume: 1, Page 4403 Paper number 1669

Abstract:

The concept of control Lyapunov function has been proven a useful tool for designing robust control laws for nonlinear systems. Recently, this concept has been extended to time-delay systems in the form of Control Lyapunov Razumikhin functions. In this paper, we further develop this extension by introducing Control Lyapunov Krasovsky functionals and show their use for robust stabilization of time-delay nonlinear systems. To further motivate the new concept we establish robustness properties for several control laws based on control Lyapunov Krasovsky functionals.

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Bifurcation Control in Systems Governed by Functional Differential Equations

Authors:

Yong Wang,

Volume: 1, Page 4409 Paper number 1687

Abstract:

This paper provides explicit sufficient conditions under which a Hopf bifurcation in systems described by functional differential equations can be stabilized. The main assumption is that the bifurcating modes are linearly unstabilizable and all other modes are linearly stabilizable. Stabilization of a Hopf bifurcation is defined as the existence of sufficiently smooth feedback control laws such that the Hopf bifurcation for the closed loop systems is supercritical. The construction of stabilizing control laws is explicit. We also give an example to illustrate the theory.

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Stabilisation Of A Class Of Nonlinear Time-Delay Systems Using Fuzzy Models

Authors:

Sing Kiong Nguang, Peng Shi,

Volume: 1, Page 4415 Paper number 1013

Abstract:

This paper examines the problem of stabilising a class of nonlinear time delay systems using fuzzy models. The class of nonlinear time delay systems under investigation is described by the Takagi-Sugeno (T-S) or Takagi-Sugeno-Kang (TSK) fuzzy model. Based on a predictor-based controller and a well-known Lyapunov functional approach, we develop a technique for designing a fuzzy state feedback control law which globally stabilises this class of nonlinear time delay systems. A numerical simulation example is presented to illustrate the theory development.

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Global Behavior In Nonlinear Systems With Delayed Feedback

Authors:

Anatoli F. Ivanov, Manuel A. Pinto, Sergei I. Trofimchuk,

Volume: 1, Page 4420 Paper number 1052

Abstract:

The problem of global stability in scalar delay differential equations of the form x'(t)=f(x(t-d)-g(x(t)) is studied. Functions f and g are continuous and such that the equation assumes a unique equilibrium. Two types of the sufficient conditions for the global asymptotic stability of the unique equilibrium are established: (i) delay independent, and (ii) conditions involving the size d of the delay. Delay independent stability conditions make use of the global stability in the limiting difference equation g(x_n+1)=f(x_n): the latter always implying the global stability in the differential equation for all values of the delay d>0. The delay dependent conditions involve the global attractivity in specially constructed one-dimensional maps (difference equations) that include the nonlinearities f and g, and the delay d.

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L_2 - L_2 and L_2-L_(infinity) Output Feedback Control of Time-Delayed LPV Systems

Authors:

Kan Tan, Karolos M. Grigoriadis,

Volume: 1, Page 4422 Paper number 1751

Abstract:

We examine the analysis and output feedback synthesis problems for linear parameter-varying (LPV) systems with parameter-varying time delays. It is assumed that the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore the stability, the L_2 induced norm performance and the L_2 to L_(infinity) gain performance of these systems using parameter-dependent Lyapunov-Krasovskii functionals. In addition, the designs of parameter-dependent dynamic output feedback controllers that guarantee stability and desired induced norm performance are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved via efficient interior-point algorithms.

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Compensation Of Input Time Delay For A Class Of Nonlinear Systems

Authors:

Lamberto Maza-Casas, Martin Velasco-Villa, Jaime Alvarez-Gallegos,

Volume: 1, Page 4428 Paper number 9151

Abstract:

A compensation strategy for nonlinear input time delay systems is considered in this work, in particular, the regulation problem is addressed. The compensation of the input time delay is based on a passivity scheme that produces, in the ideal case, a noncausal compensator. The proposed scheme can only be applied for minimum phase systems that satisfy a transversability condition. The noncausal property of the solution is tackled by approximating the ideal feedback that solves the problem by a non-anticipative one. This approximation produces an auxiliary error system that can be viewed as a perturbed system. The proposed solution is valid for a sufficient small input delay.

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Robust Control Of Uncertain Systems With Input Delay And Input Sector Nonlinearity

Authors:

Bohyung Lee, Jang Gyu Lee,

Volume: 1, Page 4430 Paper number 1821

Abstract:

In this paper, we investigate a robust control method for some nonlinear control problems with an input delay. By letting input nonlinearity in the sector bounds as a new diagonal structured uncertainty, we transform the control problems with input nonlinearity into the robust control problems of linear systems with only structured uncertainty. Applying this idea, we obtain linear matrix inequality(LMI) conditions for delay-dependent robust stabilization of structured uncertain systems with input delay and input sector nonlinearity. In addition to LMIs for the fixed input nonlinearity, we also propose an iterative LMI optimization algorithm to find robust input sector bounds such that the given uncertain system is stable for any input nonlinearity in these sector bounds.

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