Iasson Karafyllis
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
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In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system can be regarded as the feedback interconnection of a subsystem described by RFDEs and a subsystem described by FDEs. Recent Small-Gain results and Lyapunov-like characterizations of the Weighted Input-to-Output Stability property for systems described by RFDEs and FDEs are employed. It is shown that the stability results provided in this work can be used to …
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin functions of uniform and non-uniform in time Robust Global Asymptotic Output Stability and Input-to-Output Stability are given. The results of this work have been developed for systems with outputs in abstract normed linear spaces in order to allow outputs with no delay, with discrete or distributed delay or functional outputs with memory.
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to disturbances) local, semi-global, and global exponential stability, through the existence of coercive and non-coercive Lyapunov functionals. The importance of the obtained results is underlined through some applications concerning 1) exponential stability of nonlinear retard…
In this paper we show that the existence of a Lyapunov-Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability of time-invariant systems described by neutral functional differential equations in Hale's form. It is assumed that the difference operator is linear and strongly stable, and that the map in the right-hand side of the equation is Lipschitz on bounded sets. A link between global exponential stability and input-to-state stability is also provided. @ The extended version of this paper has been submitted …
We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions recently described in \cite{SunWang} for the existence of L-K functionals. We also provide related conditions for positive coupled differential-difference positive systems and for systems of neutral type that are not necessarily positive. Finally, corresponding results for discrete-time systems are described.
In this paper, we show that an infinite network of input-to-state stable (ISS) subsystems, admitting ISS Lyapunov functions, itself admits an ISS Lyapunov function, provided that the couplings between the subsystems are sufficiently weak. The strength of the couplings is described in terms of the properties of an infinite-dimensional nonlinear positive operator, built from the interconnection gains. If this operator induces a uniformly globally asymptotically stable (UGAS) system, a Lyapunov function for the infinite network can be constructed. We analyze necessary and sufficient conditions fo…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov-Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach the initi…
For discrete-time systems, governed by Kraus maps, the work of D. Petz has characterized the set of universal contraction metrics. In the present paper, we use this characterization to derive a set of quadratic Lyapunov functions for continuous-time systems, governed by Lindblad differential equations, that have a steady-state with full rank. An extremity of this set is given by the Bures metric, for which the quadratic Lyapunov function is obtained by inverting a Sylvester equation. We illustrate the method by providing a strict Lyapunov function for a Lindblad equation designed to stabilize …
This article concerns robustness analysis for interconnections of two dynamical systems (described by upper semicontinuous differential inclusions) using a generalized notion of derivatives associated with locally Lipschitz Lyapunov functions obtained from a finite family of differentiable functions. We first provide sufficient conditions for input-to-state stability (ISS) for differential inclusions, using a class of non-smooth (but locally Lipschitz) candidate Lyapunov functions and the concept of Lie generalized derivative. In general our conditions are less conservative than the more commo…
The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $α\in (0, 1).$ The goal of the first (second) player is to minimize (maximize) the value of a given quality index. The main contribution of the paper is the proof of the fact that this differential game has the value, i.e., the lower and upper game values coincide. The proof is based on the appropriate approximation of the game by a zero-sum differential game in which the dynamical system is described by a first order function…
In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function.
This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The objective consists of developing numerically tractable conditions ensuring the global asymptotic stability of the unique equilibrium point. The proposed approach merges two intermediate results: The first one relies on the characterization of an attractor around the origin, to which converges the closed-loop trajectories. The second result assesses the regional …
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $α\in (0, 1).$ Basing on the finite-difference Grünwald-Letnikov formulas, we propose an approximation of the considered system by a system described by a functional-differential equation of a retarded type. A mutual aiming procedure between the initial conflict-controlled system and the approximating system is given that guarantees the desired proximity between their motions. This procedure allows to apply, via the approximating system, t…
A Convex Approach for Stability Analysis of Coupled PDEs using Lyapunov Functionals
本文提出一种利用正矩阵参数化函数的算法，用于分析由耦合线性偏微分方程描述的系统稳定性，通过构造具有负导数的李雅普诺夫函数，将稳定性条件转化为LMI约束，利用SOSTOOLS和SDP求解器验证。
Linear Programming based Lower Bounds on Average Dwell-Time via Multiple Lyapunov Functions
针对切换系统平均驻留时间最小下界求解难的问题，将非凸优化转化为线性规划问题，基于多Lyapunov函数给出指数稳定性下界，实验验证较现有方法有提升。
Contraction Analysis of Time-Delay Systems
本文通过微分框架扩展Lyapunov-Krasovskii泛函和Lyapunov-Razumikhin函数的概念，研究非线性时滞系统的收缩分析，并利用线性矩阵不等式设计单时滞系统的镇定反馈控制。
In (Jin, 2018), a new day-to-day dynamical system was proposed for drivers' departure time choice at a single bottleneck. Based on three behavioral principles, the nonlocal departure and arrival times choice problems were converted to the local scheduling payoff choice problem, whose day-to-day dynamics are described by the Lighthill-Whitham-Richards (LWR) model on an imaginary road of increasing scheduling payoff. Thus the departure time user equilibrium (DTUE), the arrival time user equilibrium (ATUE), and the scheduling payoff user equilibrium (SPUE) are uniquely determined by the stationar…
Edges' Riemannian energy analysis for synchronization of multi-agent nonlinear systems over undirected weighted graphs
本研究针对无向加权图下无领导者的非线性输入仿射多智能体系统，基于黎曼度量方法设计状态反馈分布式控制律，利用边拉普拉斯算子构造李雅普诺夫函数，证明系统可实现全局指数同步。
On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations
本文建立了由单个一阶双曲型偏微分方程描述的系统与由积分延迟方程描述的系统之间的等价性，并提供了系统理论结果（包括逆Lyapunov结果），通过示例表明转换可简化鲁棒反馈镇定问题的求解。
Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control
本文提出利用退出时间最优控制构造控制Lyapunov函数与稳定反馈，将计算简化为有限维非线性规划，避免维数灾难，并给出数值验证。
Forward Completeness and Applications to Control of Automated Vehicles
该研究提出开集有限维系统的宽松类Lyapunov前向完备性条件，将其用于自动驾驶车辆无车道巡航控制设计，得到可避障、适配多场景的去中心化反馈律。
This paper presents new results that allow one to address the discrete-time general nonlinear robust control problem. The uncertain system is described by a general nonlinear function set characterized by the nominal model and the corresponding modeling error bound. Traditional synthesis methods design parameters of a structured robust controller. The key aim of this paper is to find an unstructured robust controller set in the state-control space, which enlarges the estimate of the closed-loop robust domain of attraction (RDOA). Based on the interval analysis arithmetic, a numerical method to…
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