Recent questions tagged stability

The response of a discrete time system $y[n]$ obeys the following relation:\[y[n]=\frac{5}{6} y[n-1]-\frac{1}{6} y[n-2]+x[n] .\]The input to the system is $x[n]=\delta[n]...

Let $G(s)=\frac{1}{10 s^{2}}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below.Co...

Consider the system shown below.If $K>0$, which of the following describes the system?Stable, causalStable, non-causalUnstable, non-causalUnstable, causalCannot be determ...

In the case of a linear time invariant system(1) Poles in the right half plane implies Exponential decay of output(2) Impulse response zero for $t \leq 0$ impliesSystem i...

The figure is shows the block diagram representation of control system. The system in block A has an impulse response $h_{A}(t)=e^{-t} u (t)$. The system in block $B$ has...

For a feedback amplifier, the open loop transfer function has three poles at $100 \; k \; \mathrm{rad} / \mathrm{s}, 1 \; \mathrm{M} \; \mathrm{rad} / \mathrm{s}$ and $10...

The feeback control system in the figure is stable.for all $K \geq 0$only if $\mathrm{K} \geq 1$only if $0 \leq \mathrm{K}<1$only if $0 \leq K \leq 1$

The system shown in the figure is remains stable when$k<-1$$-1 < k < 1$$1 < k < 3$$k>3$

A causal $\text{LTI}$ system is described by the difference equation\[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\]The system is stable only if$|\alpha|=2, \quad|\beta|<2$$|...

The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$The range of $\mathrm{K}$ for which the system is stable is$\fr...

Despite the presence of negative feedback, control systems still have problems of instability because thecomponents used have nonlinearities.dynamic equations of the subs...

The impulse response $h(t)$ of a linear time-invariant continuous time system is described by $h(t)=\exp (\alpha t) u(t)+\exp (\beta t) u(-t)$, where $u(t)$ denotes the u...

If $s^{3}+3 s^{2}+4 s+A=0$, then all the roots of this equation are in the left half plane provided that$\mathrm{A}>12$$-3<\mathrm{A}<4$$0<\mathrm{A}<12$$5<\mathrm{A}<12$

The transfer function of a discrete time $\text{LTI}$ system is given by$$H(z)=\frac{2-\frac{3}{4} z^{-1}}{1-\frac{3}{4} z^{-1}+\frac{1}{8} z^{-2}}$$Consider the followin...

The open loop transfer function of a feedback control system incorporating a dead time element is given by$$ G(s)=\frac{K e^{-T s}}{s(s+1)} $$Where $\mathrm{K}>0$, and $\...