Related papers: On the Nonexistence of Quadratic Lyapunov Function…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the existence of complete Lyapunov functions for semiflows…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
In this technical communique, we generalize the well-known Lyapunov-based stabilizability and detectability tests for discrete-time linear time-invariant systems to polytopic linear parameter-varying systems using the class of so-called…
We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve convex optimization problems. In particular, we consider i) classes of optimization problems of…
We consider constructing Lyapunov functions for systems that are both monotone and contractive with respect to a weighted one norm or infinity norm. This class of systems admits separable Lyapunov functions that are either the sum or the…
In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar…
This paper presents some new propositions related to the fractional order $h$-difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order $h$-difference…
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for constructing explicit ranges where quadratic Lyapunov functions…
We show that existence of a global polynomial Lyapunov function for a homogeneous polynomial vector field or a planar polynomial vector field (under a mild condition) implies existence of a polynomial Lyapunov function that is a sum of…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. Tsitsiklis Lyapunov function is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of…
In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence,…
In this note we prove that the version of Newton algorithm with line search we used in [2] converges quadratically.
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…
In this paper we present an abstraction algorithm that produces a finite bisimulation quotient for an autonomous discrete-time linear system. We assume that the bisimulation quotient is required to preserve the observations over an…
We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of…
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…
This paper proves that there does not exist a polynomial-time algorithm to the the subset sum problem. As this problem is in NP, the result implies that the class P of problems admitting polynomial-time algorithms does not equal the class…