Structural Methods of Estimation Lyapunov Exponents Linear Dynamic System

Abstract

The problem of structural identification linear dynamic systems on the basis of the analysis Lyapunov exponent in the conditions of uncertainty is considered. The method of estimation the general solution system on the basis of application static model is developed. Defini- tion of Lyapunov exponent (LE) on the analysis of a co- efficient structural properties system is grounded. On the basis of a coefficient of structural properties the special structures reflecting change LE are introduced. The crite- rion of estimation an order system on the basis of the analysis behaviour these structures are offered. The deci- sion-making method about type of roots dynamic system on the basis of the analysis of time series and the struc- tures reflecting change LE is developed. Two approaches to an estimation of the largest LE and the Perron bottom indexes are offered. The first approach to identification of a change in a coefficient of structural properties with the help secant method for various classes of roots is ground- ed. The second approach is the structurally-frequency method grounded on definition of estimations LE by means of the analysis of local minima of structures of- fered in work. The frequency method which is a modifi- cation of a method a bar graph in the statistical theory is applied to a validation of the obtained estimations. Re- sults of simulation confirm effectiveness of the offered methods, structures and procedures.