Structural stability of linear difference equations in Hilbert space

Generalized Discrete-Time H Optimization Problem for Linear Difference Equations in Hilbert Space

In this paper the state-space solution to discretetime H optimization problem for linear timeinvariant infinite-horizon difference equations in Hilbert space and sign-indefinite cost function is proposed. The necessary and sufficient conditions as well as the parametrization of all admissible controllers are derived in terms of the stabilizing solution to the Riccati equation.

Stability of Stochastic Linear Difference Equations with Varying Delay

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary systems (see, e.g. [1-3]). One of the main problems for the theory of such systems and their applications is connected with stability [1,2]. Many stability results were obtained by the construction of appropriate Lyapunov functionals. In [4-8] the method is proposed allowing,...

Reducibility and Stability Results for Linear System of Difference Equations

Linear Difference Equations

Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...

Nonlinear Functional Integrodifferential Equations in Hilbert Space

Let X be a Hilbert space and let Ω ⊂ Rn be a bounded domain with smooth boundary ∂Ω. We establish the existence and norm estimation of solutions for the parabolic partial functional integro-differential equation in X by using the fundamental solution.