2. Prove that if one of the roots of (9.17) has positive real part then the solutions of the equation of (9.16) correspo
Posted: Wed May 11, 2022 9:46 pm
2. Prove that if one of the roots of (9.17) has positive real part then the solutions of the equation of (9.16) corresponding this root are unstable. What is the nature of the general solution z(t)?
Proof The characteristic equation of (9.16) is given by pa+am-' +...+a,=0. (9.17) Let 2...., am bem distinct roots repeated 9.....9 times respectively (9, +...+9 = n). Let 2; = Q,+ iß, j = 1,..., m. It is known that (refer to Chapter 2) x;(1) = f exp (j), OSP54,-1.
Proof The characteristic equation of (9.16) is given by pa+am-' +...+a,=0. (9.17) Let 2...., am bem distinct roots repeated 9.....9 times respectively (9, +...+9 = n). Let 2; = Q,+ iß, j = 1,..., m. It is known that (refer to Chapter 2) x;(1) = f exp (j), OSP54,-1.