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# Course detail

## Discrete Methods in Civil Engineering II

Subjet code : FAST-DA59 Faculty of Civil Engineering 2011/2012 Yes prof. RNDr. Josef Diblík, DrSc. Institute of Mathematics and Descriptive Geometry Doctoral full-time study Czech n. a. examination 2 winter optional

The study programmes with the given course

 Objective of the course – aims of the course unit: The purpose of continuation of this course is analysis of stability of linear and non-linear discrete systems and methods of their applications. Objective of the course – learning outcomes and competences: n. a. Prerequisites: The ability to orientate in the basic notions and problems of discrete and difference equations. Solving problems in the areas cited in the annotation. Course contents (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. Teaching methods and criteria: n. a. Assesment methods and criteria linked to learning outcomes: Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year. Course curriculum: 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. Specification of controlled education, way of implementation and compensation for absences: Extent and forms are specified by guarantor’s regulation updated for every academic year. Recommended reading: Saber, Elaydi, N.: An Introduction to Difference Equations. Springer-Verlag 2010

Type of course unit:
Lecture: 39 hours, optionally prof. RNDr. Josef Diblík, DrSc.