Related papers: Characterizations of input-to-state stability for …
This paper is devoted to two issues. One is to provide Lyapunov-based tools to establish integral input-to-state stability (iISS) and input-to-state stability (ISS) for some classes of nonlinear parabolic equations. The other is to provide…
The distinction between conditional, unconditional, and absolute convergence in infinite-dimensional spaces has fundamental implications for computational algorithms. While these concepts coincide in finite dimensions, the Dvoretzky-Rogers…
This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…
Input-to-state stability estimates with respect to small initial conditions and input functions for infinite-dimensional systems with bilinear feedback are shown. We apply the obtained results to controlled versions of a viscous Burger…
This paper presents a synchronization criterion for networks of infinite-dimensional linear systems, extending a previous result for finite-dimensional systems. Our result, established in the general framework of input-output relations,…
Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…
We analyze the robustness of the exponential stability of infinite-dimensional sampled-data systems with unbounded control operators. The unbounded perturbations we consider are the so-called Desch-Schappacher perturbations, which arise,…
In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of $L^1$-to-$L^1$ input-output stability (abbreviated LILO). We show that in the case of finite-dimensional input and output…
In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time conditions. To establish ISS…
Selected results for the stability and optimal control of abstract switched systems in Banach and Hilbert space are reviewed. The dynamics are typically given in a piecewise sense by a family of nonlinearly perturbed evolutions of strongly…
In this paper, we investigate the well-posedness and positivity property of infinite-dimensional linear system with unbounded input and output operators. In particular, we characterize the internal and external positivity for this class of…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS).…
This work aims to synthesize a controller that ensures that an unknown discrete-time system is incrementally input-to-state stable ($\delta$-ISS). In this work, we introduce the notion of $\delta$-ISS control Lyapunov function…
We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
The aggressive integration of distributed renewable sources is changing the dynamics of the electric power grid in an unexpected manner. As a result, maintaining conventional performance specifications, such as transient stability, may not…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
Pointwise-in-time stability notions for Ordinary Differential Equations (ODEs) provide quantitative metrics for system performance by establishing bounds on the rate of decay of the system state in terms of initial condition -- allowing…