Authors:
Jure Medanic,
Volume: 1, Page 3375 Paper number 42
Abstract:
Integral transformations are applied to a fourth order nonlinear system
with two nonlinearities. The stabilizing control is developed based
on an asymptotic analysis that defines the appropriate controller structure,
one in which all variables remain bounded and approach well defined
limits. The results are generalized to higher order systems with a
similar structure, and are the basis for the design of a dynamic controller
to stabilize a related class of nonlinear systems.
Authors:
Enric C. Fossas,
Jaume B. Franch,
Sunil K. Agrawal,
Volume: 1, Page 3381 Paper number 1475
Abstract:
This communication deals with the problem of linearization by prolongations
of two-input driftless systems. For general two-input systems, the
number of computations needed to check if a system is linearizable
by prolongations is quite large. However, for driftless systems, the
conditions presented in this paper require very few computations. The
methodology is illustrated for some engineering systems which fulfill
these conditions, e.g., a unicycle, a planar robot, and a hopping robot.
Authors:
Krishna K. Busawon,
Volume: 1, Page 3386 Paper number 123
Abstract:
In this paper, we present a new control design strategy for a class
of single-input nonlinear dynamical systems. The design consists in
transforming the system into a new controllable canonical form which
we call the Jordan controllable canonical form (JCCF). In fact, the
Brunowski controllable canonical form is an special case of the JCCF.
We first show that any controllable pair can be transformed into the
JCCF. We next, extend the result to a controllable pair which is state
dependent. Using this extended Jordan controllable canonical form
we propose a control design strategy for a class of single-input control
affine systems. The design is simple and systematic and provides two
degrees of freedom to fix the convergence of the closed-loop system.
An example is given to illustrate the control design.
Authors:
Francesco Bullo,
Volume: 1, Page 3392 Paper number 1360
Abstract:
This paper presents a series expansion for the evolution of nonlinear
systems which are analytic in the state and linear in the controls.
An explicit recursive expression is obtained assuming that the input
vector fields are constant. Additional simplifications take place in
the analysis of systems described by second order polynomial vector
fields. Sufficient conditions are derived to guarantee uniform convergence
over the finite and infinite time horizon. The treatment relies only
on elementary notions on analytic functions, number theory and operator
norms.
Authors:
Guido Herrmann,
Sarah K. Spurgeon,
Christopher Edwards,
Volume: 1, Page 3398 Paper number 9504
Abstract:
This paper considers the input-output stability of exponentially stable,
non-linear systems with sampled-data output. Results for linear systems
are generalized showing that the Lp-gain with respect to the sampled-data
output exists and converges to the Lp-gain associated with the continuous-time
output when the sampling period approaches +0. The results are applied
to a non-linear control configuration and compared to a Lyapunov function
analysis based approach previously developed for a non-linear sliding-mode
like control. In contrast to the Lyapunov function technique, the sampling-time
constraint vanishes for a stable plant if no control is used.
Authors:
Ülle Kotta,
Volume: 1, Page 3404 Paper number 1863
Abstract:
The purpose of this paper is to present a new necessary and sufficient
condition for irreducibility of nonlinear input-output (i/o) difference
equation which extends directly the corresponding condition for the
linear case. The condition is presented in terms of the common left
factors of two polynomials describing the behavior of the system; the
basic difference is that unlike the linear case the polynomials related
to the nonlinear system belong to a non-commutative polynomial ring.
This condition provides a bases for finding the minimal (irreducible)
equivalent representation of the i/o equation which is a suitable starting
point for constructing a minimal state space representation.
Authors:
Lars Grüne,
Volume: 1, Page 3409 Paper number 8
Abstract:
We show that for any asymptotically controllable homogeneous system
in euclidian space (not necessarily Lipschitz at the origin) there
exists a homogeneous control Lyapunov function and a homogeneous, possibly
discontinuous state feedback law stabilizing the corresponding sampled
closed loop system. We also show the relation between the degree of
homogeneity and the bounds on the sampling rates which ensure asymptotic
stability.
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