Related papers: Partial Stability Concept in Extremum Seeking Prob…
This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is…
We study the problem of mean-square exponential incremental stabilization of nonlinear systems over uncertain communication channels. We show the ability to stabilize a system over such channels is fundamentally limited and the channel…
Neural-network-based controllers (NNCs) can represent complex, highly nonlinear control laws, but verifying the closed-loop stability of dynamical systems using them remains challenging. This work presents contributions to a…
This paper addresses the design and analysis of an extremum-seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by complex-valued partial differential equations (PDEs) of Schrodinger type.…
This paper deals with learning stability of partially observed switched linear systems under arbitrary switching. Such systems are widely used to describe cyber-physical systems which arise by combining physical systems with digital…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
The nervous system reorganizes memories from an early site to a late site, a commonly observed feature of learning and memory systems known as systems consolidation. Previous work has suggested learning rules by which consolidation may…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth --…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…
Lyapunov stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of stability…
This article aims at providing a unified analysis of the exponential stabilization of some abstract infinite dimensional systems undergoing an event-triggering mechanism that samples the control input. The partial differential equation is…
Asymptotic stability in economic receding horizon control can be obtained under a strict dissipativity assumption, related to positive-definiteness of a so-called rotated cost, and through the use of suitable terminal cost and constraints.…
Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more…