Related papers: A Piecewise Smooth Control-Lyapunov Function Frame…
Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new…
This paper addresses the stabilisation of discrete-time switching linear systems (DTSSs) with control inputs under arbitrary switching, based on the existence of a common quadratic Lyapunov function (CQLF). The authors have begun a line of…
This paper proposes a line integral Lyapunov function approach to stability analysis and stabilization for It\^o stochastic T-S models. Unlike the deterministic case, stability analysis of this model needs the information of Hessian matrix…
A DC microgrid is a promising alternative to the traditional AC power grid, since it can efficiently integrate distributed and renewable energy resources. However, as an emerging framework, it lacks the rigorous theoretical guarantees of…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an…
This paper is devoted to the stabilization problem for nonlinear driftless control systems by means of a time-varying feedback control. It is assumed that the vector fields of the system together with their first order Lie brackets span the…
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…
The dead-zone is one of the most common hard nonlinearities in industrial actuators and its presence may drastically compromise control systems stability and performance. In this work, an adaptive variable structure controller is proposed…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
This SSFG Lp stability theorem can predict permissible forcing amplitudes below which a finite nonlinear input-output gain can be maintained. Our analysis employs Linear Matrix Inequalities (LMI) and Sum-of-Squares (SOS) as the primary…
We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal…
Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the…
A combination of control Lyapunov functions (CLFs) and control barrier functions (CBFs) forms an efficient framework for addressing control challenges in safe stabilization. In our previous research, we developed an analytical control…
The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
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…
In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the…
We present a framework based on multiple Lyapunov functions to find probabilistic data-driven guarantees on the stability of unknown constrained switching linear systems (CSLS), which are switching linear systems whose switching signal is…