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This paper is concerned with robust instability analysis for linear multi-agent dynamical systems with cyclic structure. This relates to interesting and important periodic oscillation phenomena in biology and neuronal science, since the…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…
This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Model Predictive Control (MPC) is widely recognized for its ability to explicitly handle system constraints. In practice, system states are often affected by disturbances with unknown distributions. While robust MPC guarantees constraint…
We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on dissipativity theory. Applications are given to convergence rates for certain perturbations of the damped harmonic oscillator.
We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is…
Unlike traditional model-based reinforcement learning approaches that estimate system parameters from data, non-model-based data-driven control learns the optimal policy directly from input-state data without any intermediate model…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
Iterative Learning Control (ILC) enables high control performance through learning from measured data, using only limited model knowledge in the form of a nominal parametric model. Robust stability requires robustness to modeling errors,…
This paper is concerned with robust instability analysis of linear feedback systems subject to a dynamic uncertainty. The work is motivated by, and provides a basic foundation for, a more challenging problem of analyzing persistence of…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
In this paper, incremental exponential asymptotic stability of a class of switched Carath\'{e}odory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients…
This paper studies data-driven iterative learning control (ILC) for linear time-invariant (LTI) systems with unknown dynamics, output disturbances and input box-constraints. Our main contributions are: 1) using a non-parametric data-driven…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…