465 research outputs found
On convergence of infinite matrix products with alternating factors from two sets of matrices
We consider the problem of convergence to zero of matrix products
with factors from two sets of matrices,
and , due to a suitable choice of
matrices . It is assumed that for any sequence of matrices
there is a sequence of matrices such that the
corresponding matrix product converges to zero.
We show that in this case the convergence of the matrix products under
consideration is uniformly exponential, that is, , where the constants and
do not depend on the sequence and the corresponding sequence
.Comment: 7 pages, 13 bibliography references, expanded Introduction and
Section 4 "Remarks and Open Questions", accepted for publication in Discrete
Dynamics in Nature and Societ
On stabilizability of switched differential algebraic equations
This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. This geometric approach can also be utilized to derive a novel characterization of controllability
On the stabilization of persistently excited linear systems
We consider control systems of the type , where
, is a controllable pair and is an unknown
time-varying signal with values in satisfying a persistent excitation
condition i.e., \int_t^{t+T}\al(s)ds\geq \mu for every , with
independent on . We prove that such a system is stabilizable
with a linear feedback depending only on the pair if the eigenvalues
of have non-positive real part. We also show that stabilizability does not
hold for arbitrary matrices . Moreover, the question of whether the system
can be stabilized or not with an arbitrarily large rate of convergence gives
rise to a bifurcation phenomenon in dependence of the parameter
Dynamics and control of a class of underactuated mechanical systems
This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable
Stabilization of systems with asynchronous sensors and controllers
We study the stabilization of networked control systems with asynchronous
sensors and controllers. Offsets between the sensor and controller clocks are
unknown and modeled as parametric uncertainty. First we consider multi-input
linear systems and provide a sufficient condition for the existence of linear
time-invariant controllers that are capable of stabilizing the closed-loop
system for every clock offset in a given range of admissible values. For
first-order systems, we next obtain the maximum length of the offset range for
which the system can be stabilized by a single controller. Finally, this bound
is compared with the offset bounds that would be allowed if we restricted our
attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015
American Control Conference, July 1-3, 2015, the US
Formal synthesis of stabilizing controllers for periodically controlled linear switched systems
In this paper, we address the problem of synthesizing periodic switching controllers for stabilizing a family of linear systems. Our broad approach consists of constructing a finite game graph based on the family of linear systems such that every winning strategy on the game graph corresponds to a stabilizing switching controller for the family of linear systems. The construction of a (finite) game graph, the synthesis of a winning strategy and the extraction of a stabilizing controller are all computationally feasible. We illustrate our method on an example
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