4. Analyze the stability of the following LTI systems. (a) (5 points) = (1) (b) (10 points) 2 5 5 -2 -4 -4 2 1 2) (c) (1

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4 Analyze The Stability Of The Following Lti Systems A 5 Points 1 B 10 Points 2 5 5 2 4 4 2 1 2 C 1 1 (65.42 KiB) Viewed 52 times

4. Analyze the stability of the following LTI systems. (a) (5 points) = (1) (b) (10 points) 2 5 5 -2 -4 -4 2 1 2) (c) (10 points) = -5-9-11 -1 -3 -3 3 7 7 r (3) (d) (10 points) - 2 -1 1 -3 -1 6 5 5 2 (4) 4 The stability of an LTI system given in the form i = Ax can be determined by analyzing the eigenvalues, li, of A. The system is stable iff for all eigenvalues Re(li) < 0, and for all Re(i) = 0 with algebraic multiplicity qi > 2, rank(A-\;I) = n- qi (i.e. geometric and algebraic multiplicity of eigenvalues are equal) where n is the state-space dimension. The system is asymptotically stable iff for all eigenvalues Reli) <0. For an LTI system asymptotic and exponential stability are equivalent.