We prove new necessary and sufficient conditions for uniform asymptotic stability under arbitrary switching of two-dimensional switched homogeneous systems with a finite number of subsystems using a worst-case switching analysis. The novelty of our approach is in its explicit nature, which allows us to then study in detail the codimension-one bifurcations of stability of the origin in switched linear systems and further conclude new local and global stability results for certain classes of nonlinear switched systems. In particular, we formulate an analogue of Lyapunov's indirect method for $\mathcal{C}^{1}$ switched nonlinear systems and derive a new method for determining the existence of a bounded basin of attraction for a class of switched nonlinear systems.
We consider the uniform exponential stability analysis of infinite-dimensional impulsive systems defined on a Banach or Hilbert space, whose flow is governed by a fixed $C_0$-semigroup generator and whose jumps occur at a prescribed time sequence. While the flow and jump maps are…
We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a planar homogeneous cubic polynomial vector field with integer coefficients. It admits no positive de…
This paper introduces the voltage stability kernel (VSK), a cofactor-based bus-wise representation of voltage stability in lossy power systems. The VSK is defined as the vector of principal cofactors of the voltage stability Laplacian (VSL), a reduced Jacobian that retains voltag…
Streaming contraction certificates, which determine in real time whether observed data is sufficient to certify a safe control action, face two structural challenges: the disturbance distribution shifts during operation, and the system consists of coupled subsystems whose joint m…
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…
Networked SEIR models describe epidemic spread within and between interacting subpopulations through contact-supported nonlinear transmission. Standard polynomial liftings based on complete ordered Kronecker tensors yield linear higher-dimensional representations, but their dimen…