线性系统课后答案第5章.docVIP

5.1 Is the network shown in Fing5.2 BIBO stable ? If not , find a bounded input that will excite an unbound output 图5.2 的网络BIBO 是否稳定?如果不是.请举出 一般激励无界输出的有界输入. From Fig5.2 .we can obtain that Assuming zero initial and applying Laplace transform then we have because =1+ =1+ =1+ =1+2= Which is not bounded .thus the network shown in Fin5.2 is not BIBO stable ,If u(t)=sint ,then we have y(t)== we can see u(t)is bounded ,and the output excited by this input is not bounded 5.2 consider a system with an irrational function .show that a necessary condition for the system to be BIBO stable is that |g(s)| is finite for all Res 0 一个系统的传递函数是S的非有理式。证明该系统BIBO 稳定的一个必要条件是对所有Res0. |g(s)|有界。 Proof let s=then If the system is BIBO stable ,we have . for some constant M which implies shat is convergent . For all Res=We have |g(t) |g(t0 so and are also convergent , that is . where N and L are finite constant. Then | is finite ,for all Res . Another Proof, If the system is BIBO stable ,we have for some constant M .And . For all Res . We obtain |. That is . | is finite for all Res 5.3 Is a system with impulse g(t)=BIBO stable ? how about g(t)=t for t 脉冲响应为个g(t)= 的系统是否BIBO 稳定? 的系统又如何? Because the system with impulse response g(t)= is not BIBO stable ,while the system with impulse response g(t)= for is BIBO stable. 5．4 Is a system with transfer function BIBO stable 一个系统的传递函数为 ，问该系统是否BIBO 稳定。 Laplace transform has the property . If then We know . Thus So the impulse response of the system is . for the system is BIBO stable 5.5 Show that negative-feedback shown in Fig . 2.5(b) is BIBO stable if and only if and the gain a has a magnitude less than 1.For a=1 ,find a bounded input that will excite an unbounded output. 证明图2.5(b) 中的负反馈系统BIBO 稳定当且增到a 的模小于1。对于a=1情况，找出一有界输入r(t), 她所产生的输出是无界的。 Poof,If r(t)= .then the output is the impulse response of the system and equal = the im