A Bound on the Real Stability Radius of Continuous-Time by Bobylev N. A., Bulatov V.

By Bobylev N. A., Bulatov V.

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Extra resources for A Bound on the Real Stability Radius of Continuous-Time Linear Infinite-Dimensional Systems

Sample text

This is a function of band c. Next calculate the values of band c for which this estimator of (J2 is the minimum. These steps will be dealt with in detail in the sequel. Re Step 1 This problem can be solved as follows. 4). l+ (~C) + [I... 10) in which e represents an arbitrarily chosen (mk) vector. 13) we see that d is directly dependent on C. 20) to vecit = (Im®X+)vecY-[(b'Db)-1(M- 1)bb'®X+] vecY+ +[1... 6), we use for the estimator of (J2 that had to be minimized, the well-known least-squares estimator.

With the aid of this f2' the estimator of Y 2 , is calculated. 2. f2 and Xl are treated as explanatory variables and Yl as the dependent variable, and the least square estimators 52 and c are calculated. The following cases can now be described: a. The estimated dependent variables in the equation to be estimated are multicollinear; the explanatory variables are not multicollinear. This multicollinearity may be due to the dependent variables appearing in the equation being multicollinear, since 1'"2 is found by projecting the column vectors of Y 2 onto the space spanned by the column vectors of X.

With the aid of this f2' the estimator of Y 2 , is calculated. 2. f2 and Xl are treated as explanatory variables and Yl as the dependent variable, and the least square estimators 52 and c are calculated. The following cases can now be described: a. The estimated dependent variables in the equation to be estimated are multicollinear; the explanatory variables are not multicollinear. This multicollinearity may be due to the dependent variables appearing in the equation being multicollinear, since 1'"2 is found by projecting the column vectors of Y 2 onto the space spanned by the column vectors of X.

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