Related papers: On Structured Lyapunov Functions and Dissipativity…
Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…
In this brief note, we investigate some constructions of Lyapunov functions for stochastic discrete-time stabilizable dynamical systems, in other words, controlled Markov chains. The main question here is whether a Lyapunov function in some…
This paper deals with stabilization of discrete-time switched linear systems when explicit knowledge of the state-space models of their subsystems is not available. Given the set of admissible switches between the subsystems, the admissible…
The dissipativity concept sits at the intersection of physics, systems theory, and control engineering, as a natural generalisation of passive systems that dissipate energy. It relates the external behavior of systems to their internal…
By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide…
This paper investigates the stability and stabilization of diffusively coupled network dynamical systems. We leverage Lyapunov methods to analyze the role of coupling in stabilizing or destabilizing network systems. We derive critical…
This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified…
We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class, the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies…
In this paper, a method is presented to synthesize neural network controllers such that the feedback system of plant and controller is dissipative, certifying performance requirements such as L2 gain bounds. The class of plants considered…
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…
Discrete-time systems cannot be passive unless there is a direct feedthrough from the input to the output. For passivity-based control to be exploited nevertheless, some authors introduce virtual outputs, while others rely on…
This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…
In this work, we introduce a compositional framework for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on the joint dissipativity-type…
We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…
We rigorously show that dissipatively driven Frenkel-Kontorova models with either uniform or time-periodic driving asymptotically synchronize for a wide range of initial conditions. The main tool is a new Lyapunov function, as well as a 2D…
This article investigates the consensus tracking problem of multi-agent systems under jointly connected topology through automated synthesis of Lyapunov functions. Based on the proposed distributed nonlinear control protocol, several…
Dissipation in amorphous solids at low frequencies is commonly attributed to activated transitions of isolated two-level systems (TLS) that come in resonance with elastic or electric fields. Materials with low mechanical or dielectric loss…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
Lyapunov functions are essential tools in dynamical systems, as they allow the stability analysis of equilibrium points without the need to explicitly solve the system's equations. Despite their importance, no systematic method exists for…