4,935 research outputs found
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
Dynamics of Coupled Maps with a Conservation Law
A particularly simple model belonging to a wide class of coupled maps which
obey a local conservation law is studied. The phase structure of the system and
the types of the phase transitions are determined. It is argued that the
structure of the phase diagram is robust with respect to mild violations of the
conservation law. Critical exponents possibly determining a new universality
class are calculated for a set of independent order parameters. Numerical
evidence is produced suggesting that the singularity in the density of Lyapunov
exponents at is a reflection of the singularity in the density of
Fourier modes (a ``Van Hove'' singularity) and disappears if the conservation
law is broken. Applicability of the Lyapunov dimension to the description of
spatiotemporal chaos in a system with a conservation law is discussed.Comment: To be published in CHAOS #7 (31 page, 16 figures
Robust constrained model predictive control based on parameter-dependent Lyapunov functions
The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques
Issues in the design of switched linear systems : a benchmark study
In this paper we present a tutorial overview of some of the issues that arise in the design of switched linear control systems. Particular emphasis is given to issues relating to stability and control system realisation. A benchmark regulation problem is then presented. This problem is most naturally solved by means of a switched control design. The challenge to the community is to design a control system that meets the required performance specifications and permits the application of rigorous analysis techniques. A simple design solution is presented and the limitations of currently available analysis techniques are illustrated with reference to this example
Survey of Gain-Scheduling Analysis & Design
The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has
been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide
application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending
back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of
the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in
interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling
literature therefore seems both timely and appropriate. The scope of this paper includes the main
theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition
of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a
useful entry point into the relevant literature
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