Related papers: Linear Invariants for Linear Systems
A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…
This paper provides a necessary and sufficient condition for guaranteeing exponential stability of the linear difference equation $x(t)=Ax(t-a)+Bx(t-b)$ where $a>0,b>0$ are constants and $A,B$ are $n\times n$ square matrices, in terms of a…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
In this article, we introduce the notion of differential flatness by pure prolongation: loosely speaking, a system admits this property if, and only if, there exists a pure prolongation of finite order such that the prolonged system is…
We consider systems of linear partial differential equations, which contain only second and first derivatives in the $x$ variables and which are uniformly parabolic in the sense of Petrovski\v{\i} in the layer ${\mathbb R}^n\times [0,T]$.…
We call a system super-linearizable if it admits finite-dimensional embedding as a linear system -- known as a finite-dimensional Koopman embedding; said otherwise, if its dynamics can be linearized by adding a finite set of observables. We…
In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
Program invariants are important for defect detection, program verification, and program repair. However, existing techniques have limited support for important classes of invariants such as disjunctions, which express the semantics of…
The flow of contracting systems contracts 1-dimensional parallelotopes, i.e., line segments, at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an…
We state necessary and sufficient conditions to uniquely identify (modulo state isomorphism) a linear time-invariant minimal input-state-output system from finite input-output data and upper- and lower bounds on lag and state space…
We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…
Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…
This paper studies the variation diminishing property of $k$-positive linear time-invariant (LTI) systems, which map inputs with $k-1$ sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.
Let X be a smooth projective complex variety, and L a line bundle on X . We say that the linear system |L| has maximal variation if its elements have the maximum number dim|L| of moduli. We discuss some cases where this situation is…
An integer linear system is a set of inequalities with integer constraints. The solution graph of an integer linear system is an undirected graph defined on the set of feasible solutions to the integer linear system. In this graph, a pair…
This paper addresses the issue of lemma generation in a k-induction-based formal analysis of transition systems, in the linear real/integer arithmetic fragment. A backward analysis, powered by quantifier elimination, is used to output…