Questions tagged [stability]
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158 questions
0 votes
0 answers
29 views
What does a 0 in the last row of a Routh Table mean?
What does a 0 in the last row of a Routh Table mean? If there are sign changes prior, does the 0 at the end provide any new conclusions (apart from a sign change) If there are no sign changes, does ...
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2 votes
2 answers
166 views
Does $\mathrm{Re}\{{H(e^{j \omega})}\} < 1$ guarantee closed-loop stability if $H(z)$ is a real-coefficient FIR filter?
I’m analysing the discrete-time feedback system $$ T(z) = \frac{1}{1 – H(z)}, \\ H(z) = \sum_{k=1}^{N} h[k] z^{-k}, h[k] \in \mathbb{R}, N ≥ 1 $$ Thus, $H(z)$ is a strictly causal FIR with ...
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2 votes
1 answer
101 views
Why does stability of an LTI-system imply that the fourier transform of the impulse reponse is defined?
An LTI system is stable iff the fourier transform of the impulse response is defined. I know that if the fourier transform is defined the Dirichlet conditions apply. One of these conditions is ...
0 votes
1 answer
170 views
Absolute integrability and transfer function evaluated at $j\omega$
It's well-known that an LTI system is BIBO-stable if and only if its impulse response $h(t)$ is absolutely integrable: $$\text{BIBO system} \iff \int_{-\infty}^{+\infty} |h(t)|\mathrm{d}t \lt \infty$$...
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37 views
How can I show that the following system is stable?
Hi so we have a sinus signal that is sent to a feedback loop system and I'm trying to understand signals and stability better. I let $\arg(G_o(iw_o))=0$ and get that $y$ has no bound although $r=0$. ...
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2 votes
1 answer
339 views
How is causality in Laplace transform related to Fourier transform?
Taking the Laplace transform of a system given by a differential equation yields its transfer function $H(s)$. The region of convergence of the causal impulse response of the system lies right of the ...
- 123
0 votes
1 answer
46 views
Stability of pure(ideal) integrator and pure(ideal) differentiator in BIBO sense?
How to realize Poles and zeros at infinity??especially through transfer function? I was going through above Question and what i am able to understand both pure(ideal) integrator and pure(ideal) ...
- 1,992
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1 answer
81 views
Why MATLAB is considering this differentiator to be stable?
I have a MATLAB code for differentiator , it last line command isstable determines whether system is stable or not. I was surprised by response of MATLAB as according to my understanding ...
- 1,992
1 vote
1 answer
181 views
Determining stability of second order IIR filter implemented in single precision floating point
I have a second order IIR filter with DC-notch-like characteristics: $H(z) = \frac{1-2z^{-1} + z^{-2}}{1+a_1z^{-1}+a_2z^{-2}}$ where $a_1= -1.99396970948671$ and $a_2=0.994002716421032$. The filter is ...
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3 votes
1 answer
131 views
What does stability of an LTI system guarantee
I am working through some example problems about stability in systems and came across this one that I can't find the answer to. I'm wondering whether I am misunderstanding something about the ...
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2 votes
3 answers
481 views
System instability when using FIR filter in feedback loop for removing targets in FMCW radar return
I have an FMCW radar I am working on where I am also attempting to remove a specific target from the received signal (before it is sampled by the ADC). To do so, during each FMCW sweep, I am ...
0 votes
1 answer
63 views
Connection between positive feedback at DC and real-axis right-half-plane pole(s)
(Context provided here, question summarized at the end.) Suppose I have an open-loop transfer function with two coincident left half plane poles like $$ H(j\omega)=\frac{-H_0}{(1+j\omega RC)^2} $$ ...
- 349
0 votes
1 answer
264 views
Inverse of a causal and stable system
Consider a discrete-time causal and stable LTI system $S_1$. The inverse system $S_2$ is defined as the system that takes the output of $S_1$ as its input and provides the input of $S_1$ as its ...
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0 votes
1 answer
150 views
Methods to determine stability of open-loop systems
Which methods can be used to analyze the stability of open-loop systems only, closed-loop systems only, and both of them? As far as I understand, you can determine the stability of open-loop and ...
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2 votes
1 answer
201 views
Does the impulse response of every stable system have finite energy?
I need to show that the impulse response of every stable system has finite energy. I have trouble solving this problem. Since impulse input signal is unbounded, I can't apply BIBO stability of system ...
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