Related papers: Synthesis of Lyapunov Functions using Formal Verif…
This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…
This paper studies switching stabilization problems for general switched nonlinear systems. A piecewise smooth control-Lyapunov function (PSCLF) approach is proposed and a constructive way to design a stabilizing switching law is developed.…
Certifying the stability of dynamical systems is a central and challenging task in control theory and systems analysis. To tackle these problems we present an algorithmic approach to finding polynomial Lyapunov functions. Our method relies…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
Continuous piecewise affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then…
Safety and stability are essential properties of control systems. Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are powerful tools to ensure safety and stability respectively. However, previous approaches typically…
We present a technique for learning control Lyapunov (potential) functions, which are used in turn to synthesize controllers for nonlinear dynamical systems. The learning framework uses a demonstrator that implements a black-box, untrusted…
Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…
We present a controller synthesis algorithm for reach-avoid problems for piecewise linear discrete-time systems. Our algorithm relies on SMT solvers and in this paper we focus on piecewise constant control strategies. Our algorithm…
An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions…
This paper tackles state feedback control of switched linear systems under arbitrary switching. We propose a data-driven control framework that allows to compute a stabilizing state feedback using only a finite set of observations of…
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…
The paper deals with the problem of the sampled data feedback stabilization for autonomous nonlinear systems. The corresponding results extend those obtained in earlier works by the same authors. The sufficient conditions we establish are…
In this article, the problem of synthesizing switching controllers is considered through the synthesis of a "control certificate". Control certificates include control barrier and Lyapunov functions, which represent control strategies, and…
In this paper, the problem of assessing the Finite-Time Stability (FTS) property for general nonlinear systems is considered. First, some necessary and sufficient conditions that guarantee the FTS of general nonlinear systems are provided;…
Recently sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power…
We present a new data-driven method to provide probabilistic stability guarantees for black-box switched linear systems. By sampling a finite number of observations of trajectories, we construct approximate Lyapunov functions and deduce the…
Lyapunov functions play a fundamental role in analyzing the stability and convergence properties of optimization methods. In this paper, we propose a novel and straightforward approach for constructing Lyapunov functions for first-order…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
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…