Related papers: Feedback Stability Analysis via Dissipativity with…
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
Equilibrium-independent dissipativity (EID) is a recently introduced system property which requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic…
Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the…
In this paper, we study the boundary feedback stabilization of a quasilinear hyperbolic system with partially dissipative structure. Thanks to this structure, we construct a suitable Lyapunov function which leads to the exponential…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…
We consider an interlinked production model consisting of conservation laws (PDE) coupled to ordinary differential equations (ODE). Our focus is the analysis of control laws for the coupled system and corresponding stabilization questions…
This paper deals with classes of (de)stabilizing switching signals for switched systems. Most of the available conditions for stability of switched systems are sufficient in nature, and consequently, their violation does not conclude…
The proportional-integral-derivative (PID) controller and its variants are widely used in control engineering, but they often rely on linearization around equilibrium points and empirical parameter tuning, making them ineffective for…
We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…