Discrete-time affine systems. Given A E Rnxn and b E Rn, consider the discrete-time affine system...

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Discrete-time affine systems. Given A E Rnxn and b E Rn, consider the discrete-time affine system x(k+ 1) = Ax(k) + b. Assume A is convergent and show that (iii) limk→∞ x(k) = (In − A)-¹b for all initial conditions x(0) € R¹. - Hint: Define a new sequence y(k), k = Z₂o, by y(k) = x(k) - x* for an appropriate x*. Discrete-time affine systems. Given A E Rnxn and b E Rn, consider the discrete-time affine system x(k+ 1) = Ax(k) + b. Assume A is convergent and show that (iii) limk→∞ x(k) = (In − A)-¹b for all initial conditions x(0) € R¹. - Hint: Define a new sequence y(k), k = Z₂o, by y(k) = x(k) - x* for an appropriate x*.

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The question asks us to prove that for a discretetime affine system described by the equation xk 1 A... View the full answer