Related papers: Generalized Filippov solutions for systems with pr…
The prescribed-time stabilization problem for a general class of nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed-time…
This paper concerns two-dimensional Filippov systems --- ordinary differential equations that are discontinuous on one-dimensional switching manifolds. In the situation that a stable focus transitions to an unstable focus by colliding with…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
The sewed focus is one of the singularities of planar piecewise smooth dynamical systems. Defined by Filippov in his book 'Differential Equations with Discontinuous Righthand Sides' (Kluwer, 1988), it consists of two invisible tangencies…
Two types of general nonlinear consensus protocols are considered in this paper, namely the systems with nonlinear measurement and communication of the agents' states, respectively. The solutions of the systems are understood in the sense…
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
We set up, at the abstract Hilbert space setting, the general question on when an inverse linear problem induced by an operator of Friedrichs type admits solutions belonging to (the closure of) the Krylov subspace associated to such…
In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the…
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo…
Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user,…
Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various…
Predefined-time stability enables convergence within a user-specified time independent of initial conditions. Existing results are predominantly based on autonomous Lyapunov inequalities, where the predefined-time is realized through…
We consider a Kepler problem in dimension two or three, with a time-dependent $T$-periodic perturbation. We prove that for any prescribed positive integer $N$, there exist at least $N$ periodic solutions (with period $T$) as long as the…
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles from focus boundary equilibria in other types of…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…
An example of a time-invariant time-delay system that is uniformly globally attractive and exponentially stable, hence forward complete, but whose reachability sets from bounded initial conditions are not bounded over compact time intervals…