Related papers: Linear Invariants for Linear Systems
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verification of program loops. The problem of generating loop…
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a higher-dimensional Euclidean space. We solve this problem…
Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather…
The integrability has been playing an essential role in the field of differential equations. This property may better help us obtain the topological structure and even the global dynamics for the considered system. A system is called…
The paper continues the authors' study of the linearizability problem for nonlinear control systems. In the recent work [K. Sklyar, Systems Control Lett. 134 (2019), 104572], conditions on mappability of a nonlinear control system to a…
Linear time-invariant (LTI) systems appear frequently in natural sciences and engineering contexts. Many LTI systems are described by ordinary differential equations (ODEs). For example, biological gene regulation, analog filter circuits,…
We consider concurrent systems consisting of a finite but unknown number of components, that are replicated instances of a given set of finite state automata. The components communicate by executing interactions which are simultaneous…
A linear dynamical system is called positive if its flow maps the non-negative orthant to itself. More precisely, it maps the set of vectors with zero sign variations to itself. A linear dynamical system is called $k$-positive if its flow…
We consider $k$-positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to positive linear systems. It is well-known that stable positive linear time…
This note introduces a sufficient Linear Matrix Inequality (LMI) condition for the ultimate boundedness of a class of continuous-time dynamical systems with conic uncertain/nonlinear terms.
We consider a Lurie system obtained via a connection of a linear time-invariant system and a nonlinear feedback function. Such systems often have more than a single equilibrium and are thus not contractive with respect to any norm. We…
A linear dynamical system is called $k$-positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to the important class of positive linear systems. Since stable positive linear…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant…
Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…