36,631 research outputs found
A graph theoretic approach to input-to-state stability of switched systems
This article deals with input-to-state stability (ISS) of discrete-time
switched systems. Given a family of nonlinear systems with exogenous inputs, we
present a class of switching signals under which the resulting switched system
is ISS. We allow non-ISS systems in the family and our analysis involves
graph-theoretic arguments. A weighted digraph is associated to the switched
system, and a switching signal is expressed as an infinite walk on this
digraph, both in a natural way. Our class of stabilizing switching signals
(infinite walks) is periodic in nature and affords simple algorithmic
construction.Comment: 14 pages, 1 figur
On the D-Stability of Linear and Nonlinear Positive Switched Systems
We present a number of results on D-stability
of positive switched systems. Different classes of linear and
nonlinear positive switched systems are considered and simple
conditions for D-stability of each class are presented
Switching control for incremental stabilization of nonlinear systems via contraction theory
In this paper we present a switching control strategy to incrementally
stabilize a class of nonlinear dynamical systems. Exploiting recent results on
contraction analysis of switched Filippov systems derived using regularization,
sufficient conditions are presented to prove incremental stability of the
closed-loop system. Furthermore, based on these sufficient conditions, a design
procedure is proposed to design a switched control action that is active only
where the open-loop system is not sufficiently incrementally stable in order to
reduce the required control effort. The design procedure to either locally or
globally incrementally stabilize a dynamical system is then illustrated by
means of a representative example.Comment: Accepted to ECC 201
Input/output-to-state stability of switched systems under restricted switching
This paper deals with input/output-to-state stability (IOSS) of
continuous-time switched nonlinear systems. Given a family of systems, possibly
containing unstable dynamics, and a set of restrictions on admissible switches
between the subsystems and admissible dwell times on the subsystems, we
identify a class of switching signals that obeys these restrictions and
preserves stability of the resulting switched system. The primary apparatus for
our analysis is multiple Lyapunov-like functions. Input-to-state stability
(ISS) and global asymptotic stability (GAS) of switched systems under
pre-specified restrictions on switching signals fall as special cases of our
results when no outputs (resp., also inputs) are considered.Comment: 14 pages, no figur
Polybius and the anger of the Romans
In this paper, incremental exponential asymptotic stability of a class of switched Carathéodory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients between these norms. This model is rather general and includes the case of staircase switching signals as a special case. Sufficient conditions are derived for incremental stability allowing for the system to be incrementally exponentially asymptotically stable even if some of its modes are unstable in some time periods. Numerical examples on switched linear systems with periodic switching and on the synchronization of switched networks of nonlinear systems are used to illustrate the theoretical results
Geometric synthesis of a hybrid limit cycle for the stabilizing control of a class of nonlinear switched dynamical systems
International audienceThis paper proposes a new constructive method for synthesizing a hybrid limit cycle for the stabilizing control of a class of switched dynamical systems in IR 2 , switching between two discrete modes and without state discontinuity. For each mode, the system is continuous, linear or nonlinear. This method is based on a geometric approach. The first part of this paper demonstrates a necessary and sufficient condition of the existence and stability of a hybrid limit cycle consisting of a sequence of two operating modes in IR 2 which respects the technological constraints (minimum duration between two successive switchings, boundedness of the real valued state variables). It outlines the established method for reaching this hybrid limit cycle from an initial state, and then stablizing it, taking into account the constraints on the continuous variables. This is then illustrated on a Buck electrical energy converter and a nonlinear switched system in IR 2. The second part of the paper proposes and demonstrates an extension to IR n for a class of systems, which is then illustrated on a nonlinear switched system in IR 3
Observer design for piecewise smooth and switched systems via contraction theory
The aim of this paper is to present the application of an approach to study
contraction theory recently developed for piecewise smooth and switched
systems. The approach that can be used to analyze incremental stability
properties of so-called Filippov systems (or variable structure systems) is
based on the use of regularization, a procedure to make the vector field of
interest differentiable before analyzing its properties. We show that by using
this extension of contraction theory to nondifferentiable vector fields, it is
possible to design observers for a large class of piecewise smooth systems
using not only Euclidean norms, as also done in previous literature, but also
non-Euclidean norms. This allows greater flexibility in the design and
encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear)
systems. The theoretical methodology is illustrated via a set of representative
examples.Comment: Preprint accepted to IFAC World Congress 201
Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System
Many problems with control theory have led to investigations into
switched systems. One of the most urgent problems related to the analysis of the
dynamics of switched systems is the stability problem. The stability of a switched
system can be ensured by a common Lyapunov function for all switching modes under
an arbitrary switching law. Finding a common Lyapunov function is still an interesting
and challenging problem. The purpose of the present paper is to prove the stability of
equilibrium in a certain class of nonlinear switched systems by introducing a common
Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler
divergence or Csiszár's I-divergence between the state and equilibrium. The switched
system is useful for finding positive solutions to linear algebraic equations, which
minimize the I-divergence measure under arbitrary switching. One application of the
stability of a given switched system is in developing a new approach to reconstructing
tomographic images, but nonetheless, the presented results can be used in numerous
other areas
Robust exponential stability of nonlinear impulsive switched systems with time-varying delays
This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results
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