# Questions tagged [stability]

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63 questions
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### Is tanx(t) stable?

I am highly confused about the stability of tanx(t). If we provide a bounded input such as x[t]=u[t], the output is bounded I have confusion about stable Is the function BIBO stable and also is it ...
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### Nyquist Plot for transfer functions with poles at the origin

I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states "If f(...
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### Defining bound on input signal to test accumulator for BIBO stability

For an accumulator, defined as shown in the image below, why would I define $B_x=1$? $u[n]$ is defined at zero so my (possibly misguided intuition) is telling me that I'd choose $B_x = 0$ to not ...
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### Determine if $y[n] = ny[n-1] + x[n]$ is linear time invariant and BIBO stable

Check if the following system is linear time invariant and BIBO stable.. $$y[n] = ny[n-1] + x[n]$$ for $n\ge 0$. We are also given that the system is at rest (i.e. $y[−1] = 0$). I know that to ...
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### How to design a *desired signal* for Lyapunov stability analysis?

How to design a desired signal for Lyapunov stability analysis? Like given in this paper: http://journals.tubitak.gov.tr/elektrik/issues/elk-15-23-3/elk-23-3-8-1212-29.pdf
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### Why does stability only consider, whether the system is bounded? That doesn't mean the response is smooth?

Why does (BIBO) stability only consider, whether the system is bounded? That doesn't mean the response is smooth? That is, one could have system whose values are bounded. Still it could exhibit "...
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### Absolute Integrable Sinc function

How do we prove that $$\int_{-\infty}^{\infty}\bigg|\dfrac{\sin t}{\pi t}\bigg|dt\to \infty$$ This comes in the context of stability of LTI system with impulse response $h(t) = \dfrac{\sin t}{\pi t}$. ...
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### How to conclude LTI, causality and BIBO stability of a system represented by a differential equation?

I have started to learn about systems represented by differential equations in Oppenheim's Signals & Systems, and I got really confused about it. I am trying to understand how I can show that a ...
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### BIBO Stability of an impulse response

I am trying to prove if $h_1[n] = 2^{-n} u[n]$ and $h_2[n] = (0.1)^n$ are BIBO stable or not, but I'm not sure if these analysis are correct. I'm having some trouble to understand this specific ...
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### Does “improper” imply that a system cannot be stable and causal?

This answer and the comments in it made me wonder whether the following statement is true: If a transfer function is improper, then that system cannot be causal and stable at the same time. I had ...
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### numerical instability while solving a physical model

I am trying to solve an estimation problem and my physical model look smth like this: $A'/A^2 = B'/B^2 + C'/C^2$, from which I have measured $A$ and a reference for $B'$. I want to try adaptive ...
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### Frequency Response Question on LSI System

Someone please explain me the question its seems very complicated to me. I just want know what the question asking and how to solve it i dont want fully solved solution. Thank you!!
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### Generay way to find Stability of system

I am trying to find a general way to find system stability.I have applied these methods and struck in confusion For eg: If $$y(t)= \int_{-\infty}^{t} x(\tau) \sin(4\tau) d\tau$$ then find whether the ...
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### Stability of open-loop transfer function from its Nyquist plot

I am facing a confusion on understanding system open-loop transfer function stability from its Nyquist plot. According to the formula, for open loop transfer function stability: $$Z=N+P=0$$ where $N$ ...
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### Determine the stability of a system without using the $\mathcal Z$-transform (described by a difference equation)

For example, let's say a causal LTI System is described by the following equation: $$y[n] - ay[n-1] = x[n] - bx[n-1],\quad n \in Z$$ Is there a way to determine (in this case) the stability of the ...
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### Marginal Stability based on Poles

We know that a discrete-time system with a (Z-transform) transfer function that has a pole of magnitude 1 (i.e. $|z|=1$ is a pole of the transfer function) is marginally stable if the pole at $z=1$ is ...
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### Time-invariance, causality and stability of $h(t)$ of four given systems

Question: The impulse response functions of four linear systems $S_1,\ S_2,\ S_3,\ S_4$ are given respectively by \begin{align} h_1(t)&=1\\ h_2(t)&=u(t)\\ h_3(t)&=\frac{u(t)}{(t+1)}...
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### BIBO Stability of a piecewise function

I have a function $y$ defined as $$y(t) = \left\{\begin{array} ~t~ \mbox{ where} |t| \le 3\\ 0~ \mbox{ otherwise} \end{array} \right .$$ With a system defined as $$G(t) = ty(t),$$ is it BIBO ...
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### Transient response of system with single pole $0 \le p < 1$

$G(z) = \frac{1-p}{z-p}$ If the value of p satisfies $0 \leq p < 1$ there are no oscillations in the transient response. Question: Why is that $\uparrow$ true? I know roughly what a ...
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### How to determine the poles from a graph

From my knowledge of stability, I understand that if the function approaches a finite number then the system will be stable. Thus if a system is stable its poles will be on the left of the $j\omega$-...