3,005 research outputs found
Model Reduction of Multi-Dimensional and Uncertain Systems
We present model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation (LFT) on a repeated scalar uncertainty structure. These reduction methods can be interpreted either as doing state order reduction for multi-dimensionalsystems, or as uncertainty simplification in the case of uncertain systems, and are based on finding solutions to a pair of Linear Matrix Inequalities (LMIs). A related necessary and sufficient condition for the exact reducibility of stable uncertain systems is also presented
Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance
Diagonally dominant matrices have many applications in systems and control
theory. Linear dynamical systems with scaled diagonally dominant drift
matrices, which include stable positive systems, allow for scalable stability
analysis. For example, it is known that Lyapunov inequalities for this class of
systems admit diagonal solutions. In this paper, we present an extension of
scaled diagonally dominance to block partitioned matrices. We show that our
definition describes matrices admitting block-diagonal solutions to Lyapunov
inequalities and that these solutions can be computed using linear algebraic
tools. We also show how in some cases the Lyapunov inequalities can be
decoupled into a set of lower dimensional linear matrix inequalities, thus
leading to improved scalability. We conclude by illustrating some advantages
and limitations of our results with numerical examples.Comment: 6 pages, to appear in Proceedings of the Conference on Decision and
Control 201
Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties
Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties
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
Distributed Control of Positive Systems
A system is called positive if the set of non-negative states is left
invariant by the dynamics. Stability analysis and controller optimization are
greatly simplified for such systems. For example, linear Lyapunov functions and
storage functions can be used instead of quadratic ones. This paper shows how
such methods can be used for synthesis of distributed controllers. It also
shows that stability and performance of such control systems can be verified
with a complexity that scales linearly with the number of interconnections.
Several results regarding scalable synthesis and verfication are derived,
including a new stronger version of the Kalman-Yakubovich-Popov lemma for
positive systems. Some main results are stated for frequency domain models
using the notion of positively dominated system. The analysis is illustrated
with applications to transportation networks, vehicle formations and power
systems
H∞ control of nonlinear systems: a convex characterization
The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed
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