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This study investigates the absolute stability criteria based on the framework of integral quadratic constraint (IQC) for feedback systems with slope-restricted nonlinearities. In existing works, well-known absolute stability certificates…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulation-based…
This paper provides a link between time-domain and frequency-domain stability results in the literature. Specifically, we focus on the comparison between stability results for a feedback interconnection of two nonlinear systems stated in…
A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound on the stability number…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
A new method for the stability assessment of inverter-based microgrids is presented in this paper. Directly determining stability boundaries by searching the multidimensional space of inverters' droop gains is a computationally prohibitive…
This paper focuses on formally verifying invariant properties of control programs both at the model and code levels. The physical process is described by an uncertain discrete-time state-space system, where the dependence of the state-space…
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an…
In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
Relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi-input multi-output nonlinear plant and an integral controller. Roughly speaking, it is shown that if the composition of the plant…
Due to their relevance in systems analysis and (robust) controller design, we consider the problem of determining control-theoretic system properties of an a priori unknown system from data only. More specifically, we introduce a necessary…
The existence, uniqueness, and exponential stability results for mild solutions to the fractional neutral stochastic differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors…
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
A new method for stability assessment of inverter-based microgrids is presented in this paper. It leverages the notion of critical clusters -- a localized group of inverters with parameters having the highest impact on the system stability.…
Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints…
We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci.,…