Related papers: Stability Verification for Switched Systems using …
Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap…
Nonlinear modal decoupling (NMD) was recently proposed to nonlinearly transform a multi-oscillator system into a number of decoupled oscillators which together behave the same as the original system in an extended neighborhood of the…
Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient conditions ensure the strict compatibility of a control barrier…
Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…
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…
This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…
In this work, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of…
In this paper nonstandard finite difference (NSFD) schemes of two metapopulation models are constructed. The stability properties of the discrete models are investigated by the use of a generalization of Lyapunov stability theorem. Due to…
Control barrier functions (CBFs) have recently been introduced as a systematic tool to ensure safety by establishing set invariance. When combined with a control Lyapunov function (CLF), they form a safety-critical control mechanism.…
In this paper, we propose a Lyapunov-based reinforcement learning method for distributed control of nonlinear systems comprising interacting subsystems with guaranteed closed-loop stability. Specifically, we conduct a detailed stability…
This work makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a…
Graph Neural Networks (GNNs) are highly vulnerable to adversarial perturbations in both topology and features, making the learning of robust representations a critical challenge. In this work, we bridge GNNs with control theory to introduce…
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…
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;…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
We develop an optimization-free framework for safe stabilization of single-input control-affine nonlinear systems with a given control Lyapunov function (CLF) and a given control barrier function (CBF), where the desired equilibrium lies in…