Course detail

The purpose of continuation of this course is analysis of stability of linear and non-linear discrete systems and methods of their applications.

n. a.

The ability to orientate in the basic notions and problems of discrete and difference equations. Solving problems in the areas cited in the annotation.

The discipline is devoted to description of processes via discrete equations. It consists of three parts:
a) Stability of solutions. Stability of numerical algorithms.
b) Application of difference equations.
c) Control of processes using difference equations.

n. a.

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

a)Stability of equilibrium points. Kinds of stabily and instability.
b)Stability of linear systems with the variable matrix.
c)Stability of nonlinear systems via linearization.
d)Ljapunov direct method of stability.
e)Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points.
f) Application of difference equations
g)Discrete equivalents of continuous systems.
h)Discrete control theory.
i)The controllability and the complete controllability.
j)Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm. k)Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability.
l)Stabilization of control by feedback.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Saber, Elaydi, N.: An Introduction to Difference Equations. Springer-Verlag 2010