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.
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.
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.
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.
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.
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.
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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