For nonlinear control systems on normed vector spaces, we characterize an incremental input-to-state stability (ISS) type property in which the overshoot constant multiplies both the initial-condition and the input terms. Working through the associated variational system, we show that two properties are equivalent: an ISS-type bound on the variational system, and the incremental ISS-type bound on the original system. We further establish the equivalence between an infinitesimal contraction condition, expressed through a Lyapunov-type function, and an incremental Lyapunov condition. Each of these equivalent conditions yields a necessary condition and a sufficient condition for the ISS-type bounds, differing only in the input Lipschitz constant of the vector field. When the overshoot constant equals one, the infinitesimal contraction condition reduces to the standard norm-based contraction conditions. We establish these implications under mere continuous differentiability of the vector field, and we illustrate the results through sensitivity matrices and Lyapunov characteristic exponents. Moreover, we develop similar implications for discrete-time systems.
We study conditions under which stability of the origin of stochastic differential equations is robust to small perturbations. We express robustness in two ways, firstly in the sense that stochastic stability is maintained under small parametric perturbations not exceeding a stat…
Model Predictive Path Integral (MPPI) control is directly implementable on nonlinear systems because its online update requires only forward rollouts of the dynamics, not gradients, linearizations, or convex optimization. However, this algorithmic flexibility does not by itself p…
Stability is often assumed in learning and identification, yet it is rarely characterized directly from input--output data. We show that an input--output family admits a stable finite-dimensional state-linear realization iff it has finite Hankel-rank and its response decays unifo…
This paper provides two results that are useful in the study of the existence and the stability properties of almost periodic solutions for a given dynamical system. The obtained results are generalizations of recent results for periodic systems and are applied to the global entr…
This article develops a large-signal stability analysis for a sampled-data optimization-based secondary controller for distributed energy resources (DERs) in power systems. The induced closed loop combines nonlinear inverter power-flow dynamics, filtered active and reactive power…
Adaptive control learns the plant online; neural-operator control learns the control gains offline. We bring the two together for a class of nonlinear hyperbolic PDEs whose dynamics are governed by an unknown Volterra series of arbitrarily many kernels. An observer-based passive…