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In this paper, we study finite-time state consensus problems for continuous nonlinear multi-agent systems. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a…
The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the…
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach-avoid-stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be…
This paper addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two…
This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we…
Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions,…
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…
A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…
This paper addresses the robust consensus problem under switching topologies. Contrary to existing methods, the proposed approach provides decentralized protocols that achieve consensus for networked multi-agent systems in a predefined…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…
This paper presents new classes of consensus protocols with fixed-time convergence, which enable the definition of an upper bound for consensus state as a parameter of the consensus protocol, ensuring its independence from the initial…
This work is devoted to investigate the stability properties of time-delay reset systems. We present a Lyapunov-Krasovskii proposition, which generalizes the available results in the literature, providing results for verifying the stability…
This paper investigates the boundary stabilization of an Euler-Bernoulli beam under constant axial tension and subject to an internal time-delay. First, the well-posedness of the system is established using semigroup of linear operators…
An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays. The state of the art, ongoing…
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
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…
Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still…
This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals, Lyapunov-based sufficient…