Positive Forms and Stability of Linear Time-Delay Systems
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TLDR
An explicit parametrization of a finite-dimensional subset of the cone of Lyapunov functions is given, enforced using sum-of-squares polynomial matrices, which allows the computation to be formulated as a semidefinite program.Abstract:
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit parameterization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program.read more
Citations
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Brief paper: A novel stability analysis of linear systems under asynchronous samplings
TL;DR: This article proposes a novel approach to assess the stability of continuous linear systems with sampled-data inputs based on the discrete-time Lyapunov theorem, which provides easy tractable stability conditions for the continuous-time model.
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Hierarchy of LMI conditions for the stability analysis of time-delay systems☆
TL;DR: The present paper aims at providing a generic set of integral inequalities which are asymptotically non conservative and then to design functionals driven by these inequalities, which form a hierarchy of LMI which is competitive with the most efficient existing methods.
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Technical communique: A delay-partitioning approach to the stability analysis of discrete-time systems
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Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems
TL;DR: The proposed stability conditions characterize the pointwise decrease of a linear copositive Lyapunov function and are formulated in terms of finite-dimensional or semi-infinite linear programs for which three asymptotically exact computational methods are proposed and compared with each other on numerical examples.
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Survey on time-delay approach to networked control
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Book
Stability of Time-Delay Systems
TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
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Semidefinite programming
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Global Optimization with Polynomials and the Problem of Moments
TL;DR: It is shown that the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): R n to R, in a compact set K defined byPolynomial inequalities reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems.
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Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
TL;DR: In this paper, the authors introduce a specific class of linear matrix inequalities (LMI) whose optimal solution can be characterized exactly, i.e., the optimal value equals the spectral radius of the operator.