Related papers: Unconditionnally stable scheme for Riccati equatio…
In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of…
In this paper, we derive a Riccati-type equation applicable to (sub-)static Einstein spaces and examine its various applications. Specifically, within the framework of conformally compactifiable manifolds, we prove a splitting theorem for…
For linear time-invariant systems having a state matrix with uncertain sign, we formulate a minimax adaptive control problem as a zero sum dynamic game. Explicit expressions for the optimal value function and the optimal control law are…
We study existence and regularity properties of stable positive solutions to the nonvariational problem - Delta u - b(x)|nabla u|^2 = lambda g(u) in a bounded smooth domain. In the case where b is constant, by means of a Hopf-Cole…
We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement to track the interface position. To attain a feedback…
This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are allowed to be stiff. For a class of new ImEx multistep schemes…
A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent…
In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a…
An abstract nonautonomous parabolic linear-quadratic regulator problem with very general final cost operator P_T is considered, subject to the same assumptions under which a classical solution of the associated differential Riccati equation…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
In this paper, we tackle the significant challenge of simultaneous stabilization in control systems engineering, where the aim is to employ a single controller to ensure stability across multiple systems. We delve into both scalar and…
In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some…
Linearized numerical stability bounds for solving the nonlinear time-dependent Schr\"odinger equation (NLSE) using explicit finite-differencing are shown. The bounds are computed for the fourth-order Runge-Kutta scheme in time and both…
It is well known that Forward Time and Centred in Space (FTCS) scheme for scalar Hyperbolic Conservation Law (HCL) is unconditionally unstable. The main contribution of this work to show that FTCS is conditionally stable for HCL. A new…
We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial…
We use the Riccati equation method with other ones to establish new oscillation and interval oscillation criteria for linear matrix Hamiltonian systems. We investigate the oscillation problem for linear matrix Hamiltonian systems in a new…
We consider the application of the theory of vibrational control to H_infinity-problems. We study the possibility of introduction of high-frequency parametric vibrations in order to decrease the minimal attainable value of the…
In this paper we consider a class of conjugate discrete-time Riccati equations (CDARE), arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Recently, we have proved the existence of the…
The chaos control problem of continuous time Rabinovich chaotic system is addressed. An instantaneous control input has been designed using predictive control principle to guarantee the convergence of the chaotic trajectory towards an…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…