Consider the n-p by n observability matrix V for a DT system. Let v_i denote the
ID: 3109013 • Letter: C
Question
Consider the n-p by n observability matrix V for a DT system. Let v_i denote the ith n-dimensional row of V. Assume that the characteristic function is Delta(Z) =Z^4 + .2Z^3 - .3z^2 + .25z -.1 (a) How many rows of V, at most, can be linearly independent? (b) Let the kth block CA^k of V be denoted by V^k. Consider the augmented observability matrix V_n+1 which has an extra block. Express V^n in terms of the other blocks, if the characteristic function is that given in the problem Statement. (c) If the ith row of block V^k is denoted as v^ki, express the row v^ni in terms of other rows in V.Explanation / Answer
The roots of characteristic function are, z=0.4249000432423476, 0.15380940259023562 +i* 0.47824999428204085 , 0.15380940259023562 -i* 0.47824999428204085, -0.9325188484228188 .
Two are real distinct and two are complex roots.
since 2 distinct roots are there, so 2 rows of V at most LI