2,872 research outputs found
The Internal Model Principle for Systems with Unbounded Control and Observation
In this paper the theory of robust output regulation of distributed parameter
systems with infinite-dimensional exosystems is extended for plants with
unbounded control and observation. As the main result, we present the internal
model principle for linear infinite-dimensional systems with unbounded input
and output operators. We do this for two different definitions of an internal
model found in the literature, namely, the p-copy internal model and the
-conditions. We also introduce a new way of defining an internal
model for infinite-dimensional systems. The theoretic results are illustrated
with an example where we consider robust output tracking for a one-dimensional
heat equation with boundary control and pointwise measurements.Comment: 38 pages, 2 figures, in revie
Robustness of strong stability of semigroups
In this paper we study the preservation of strong stability of strongly
continuous semigroups on Hilbert spaces. In particular, we study a situation
where the generator of the semigroup has a finite number of spectral points on
the imaginary axis and the norm of its resolvent operator is polynomially
bounded near these points. We characterize classes of finite rank perturbations
preserving the strong stability of the semigroup. In addition, we improve
recent results on preservation of polynomial stability of a semigroup under
finite rank perturbations of its generator. Theoretic results are illustrated
with an example where we consider the preservation of the strong stability of a
multiplication semigroup.Comment: 25 pages, 2 figures, submitte
Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems
We construct two error feedback controllers for robust output tracking and
disturbance rejection of a regular linear system with nonsmooth reference and
disturbance signals. We show that for sufficiently smooth signals the output
converges to the reference at a rate that depends on the behaviour of the
transfer function of the plant on the imaginary axis. In addition, we construct
a controller that can be designed to achieve robustness with respect to a given
class of uncertainties in the system, and present a novel controller structure
for output tracking and disturbance rejection without the robustness
requirement. We also generalize the internal model principle for regular linear
systems with boundary disturbance and for controllers with unbounded input and
output operators. The construction of controllers is illustrated with an
example where we consider output tracking of a nonsmooth periodic reference
signal for a two-dimensional heat equation with boundary control and
observation, and with periodic disturbances on the boundary.Comment: 30 pages, 3 figures, to appear in SIAM Journal on Control &
Optimizatio
Robust Stability Analysis of Nonlinear Hybrid Systems
We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems
Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems
AbstractDefinitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated
Stability of Planar Nonlinear Switched Systems
We consider the time-dependent nonlinear system , where , and are two
% smooth vector fields, globally asymptotically stable at the origin
and is an arbitrary measurable function. Analysing the
topology of the set where and are parallel, we give some sufficient and
some necessary conditions for global asymptotic stability, uniform with respect
to . Such conditions can be verified without any integration or
construction of a Lyapunov function, and they are robust under small
perturbations of the vector fields
Maximizing the Closed Loop Asymptotic Decay Rate for the Two-Mass-Spring Control Problem
We consider the following problem: find a fixed-order linear controller that
maximizes the closed-loop asymptotic decay rate for the classical
two-mass-spring system. This can be formulated as the problem of minimizing the
abscissa (maximum of the real parts of the roots) of a polynomial whose
coefficients depend linearly on the controller parameters. We show that the
only order for which there is a non-trivial solution is 2. In this case, we
derive a controller that we prove locally maximizes the asymptotic decay rate,
using recently developed techniques from nonsmooth analysis
Analysis of Implicit Uncertain Systems. Part I: Theoretical Framework
This paper introduces a general and powerful framework for the analysis of uncertain systems, encompassing linear fractional transformations, the behavioral approach for system theory and the integral quadratic constraint formulation. In this approach, a system is defined by implicit equations, and the central analysis question is to test for solutions of these equations. In Part I, the general properties of this formulation are developed, and computable necessary and sufficient conditions are derived for a robust performance problem posed in this framework
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