Authors:
Andrew R. Teel,
Dragan Nesić,
Luc Moreau,
Volume: 1, Page 4361 Paper number 1177
Abstract:
We consider two different definitions of "average" for systems with
disturbances: the "strong" and "weak" averages that were recently introduced
in the literature. We generalize the existing definitions as we use
the distance to an arbitrary closed set (cal) A instead of the Euclidean
norm for states in the definitions of averages. This generalization
allows us to deal with more general cases of averaging for systems
with disturbances, such as partial averaging. Under appropriate conditions,
the solutions of a time-varying system with disturbances are shown
to converge uniformly on compact time intervals to the solutions of
the system's average as the rate of change of time increases to infinity.
Authors:
Markus Bröcker,
Jan Polzer,
Markus Lemmen,
Volume: 1, Page 4367 Paper number 1117
Abstract:
The behaviour of nonlinear systems can be affected by undesired inputs
-- the disturbances. To decrease or to decouple the influence of those
disturbances this paper deals with an advanced algorithm which solves
the disturbance decoupling problem. Based on the mathematical foundations
of differential algebra, the algorithm determines if a system is decouplable
or not and which disturbance decoupling controller can be applied.
The algorithm is restricted to rational systems. To handle analytical
systems as well, a system transformation is introduced in order to
receive a rational substitute system. The disturbance decoupling problem
can then be solved for this substitute system.
Authors:
M.K. Çamlibel,
M.K.K. Cevik,
W.P.M.H. Heemels,
J.M. Schumacher,
Volume: 1, Page 4373 Paper number 1836
Abstract:
Linear complementarity systems are used to model discontinuous dynamical
systems such as networks with ideal diodes and mechanical systems with
unilateral constraints. In these systems mode changes are modeled by
a relation between nonnegative, complementarity variables. We consider
approximating systems obtained by replacing this non-Lipschitzian relation
with a Lipschitzian function and investigate the convergence of the
solutions of the approximating system to those of the ideal system
as the Lipschitzian characteristic approaches to the (non-Lipschitzian)
complementarity relation. It is shown that this kind of convergence
holds for linear passive complementarity systems for which solutions
are known to exist and to be unique. Moreover, this result is extended
to systems that can be made passive by pole shifting.
Authors:
George J. Pappas,
Slobodan N. Simić,
Volume: 1, Page 4379 Paper number 1733
Abstract:
In this paper, we consider the problem of constructing hierarchies
of nonlinear control systems that preserve reachability properties,
and, in particular, local accessibility. In this hierarchical framework,
showing local accessibility of the higher level abstracted model of
the nonlinear control system is equivalent to showing local accessibility
of the, more detailed, lower level model. Hierarchies of consistent
nonlinear abstractions can therefore result in significant complexity
reduction in determining the reachability properties of nonlinear systems.
Authors:
W. Steven Gray,
Yuan Wang,
Volume: 1, Page 4385 Paper number 1278
Abstract:
Fliess operators as input-output mappings are particularly useful in
a number of fundamental problems concerning nonlinear realization theory.
In the classical analysis of these operators, certain growth conditions
on the coefficients in their series representations insure uniform
and absolute convergence, provided each admissible input is uniformly
bounded by some fixed upperbound. In some emerging applications of
this theory, however, it is more natural to consider other classes
of inputs. In this paper, L_p function spaces are considered. In particular,
growth conditions are developed which provide sufficient conditions
for convergence and continuity, and insure that any realization of
the operator yields a well defined state space model on the input space.
Authors:
Shahram M. Shahruz,
Volume: 1, Page 4391 Paper number 8017
Abstract:
The rate equations of a large class of lasers are considered. These
equations represent the evolution of photon and carrier densities in
the laser, where the laser output is proportional to the photon density.
By applying techniques from the theory of dynamical systems to the
rate equations, four important properties of the lasers are rigorously
proved. These properties are: (P1) for nonnegative and bounded inputs,
the laser outputs are bounded; (P2) for a positive constant input,
the laser output settles at a positive steady-state value; (P3) for
positive constant inputs, the laser does not exhibit a limit cycle
behavior; (P4) for positive constant inputs, the relaxation oscillations
in the laser output can be attenuated if the coefficient of the spontaneous
emission is increased.
Authors:
Alexander Fradkov,
Volume: 1, Page 4397 Paper number 2043
Abstract:
A framework for system analysis and design is described based on nonlinear
system models and nonperiodic signals generated by nonlinear systems.
The proposed approach to analysis of nonlinear systems is based on
excitability index - a nonlinear counterpart of magnitude frequency
response of linear system. It can be used for stability analysis of
fully nonlinear cascade systems similarly to absolute stability analysis
of Lur'e systems. Speed-Gradient algorithms of creating feedback resonance
in nonlinear multi-DOF oscillators are described. For strictly dissipative
systems bounds of energy and excitability change by feedback are established.
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