相关论文: Computation of Linear Comparison Equations for Sta…
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…
We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
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…
In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
This work estimates safe invariant subsets of the Region of Attraction (ROA) for a seven-state vehicle-with-driver system, capturing both asymptotic stability and the influence of state-safety bounds along the system trajectory. Safe sets…
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…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
Finite-time stability (FTS) of a differential equation guarantees that solutions reach a given equilibrium point in finite time, where the time of convergence depends on the initial state of the system. For traditional stability notions…
The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent…
For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Grid-synchronization stability (GSS) is an emerging stability issue of grid-tied voltage source converters (VSCs), which can be provoked by severe grid voltage sags. Although a qualitative understanding of the mechanism behind the loss of…
Hybrid systems exhibit phenomena which do not occur in systems with continuous vector fields. One such phenomenon - Zeno executions - is characterized by an infinite number of discrete events or transitions occurring over a finite interval…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and…
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…