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The system is stable at origin if for every initial state which is sufficiently close to the origin remains near the origin for all t then the system is :

The system is stable at origin if for every initial state which is sufficiently close to the origin remains near the origin for all t then the system is : Correct Answer Stable

By definition, the system is stable at origin if for every initial state which is sufficiently close to the origin remains near the origin for all t then the system is stable.

Related Questions

Consider the following statements: SCR can be turned on by 1. Applying anode voltage at a sufficiently fast rate 2. Applying sufficiently large anode voltage 3. decreasing the temperature of SCR 4. Applying sufficiently large gate current Which of the above statements are correct?
Two statements are given followed by four conclusions numbered I, II, III and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: I. Some forms are open ended. II. All close ended are forms. Conclusions: I. No open ended are forms. II. Some close ended are open ended. III. No forms are close ended. IV. All open ended are close ended.
The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| S3 : The system is neither stable nor causal for
$$ROC:{1 \over 4} Which one of the following statements is valid?
P, Q and R invested in a business for 2.5 years, such that P’s initial investment was 60% more than Q’s initial investment, while R’s initial investment was 25% less than P’s initial investment. After 10 months, each of them invested 25% of their initial investment. What part of the total profit will P received after 2.5 years?
A container of 425 liters was filled with chemicals through two pipes. The first pipe was kept open for 5 hours more than the second pipe. If the first pipe remains open for as long as the second pipe remains open, and the second pipe remains open for as long as the first pipe remains open, then the quantity of chemical filled by the first pipe was half the quantity of chemical filled by the second pipe. If both the pipes are opened simultaneously, the tank will be filled in 17 hours. For how long was the second pipe open?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
The Amazon basin has been continuously inhabited for at least 10, 000 years, possibly more. Its earliest inhabitants were stone-age peoples, living in hundreds of far-flung tribes, some tiny, others numbering in the tens of thousands. It was from the west that Europeans explorers first arrived. In 1541 a Spanish expedition from Quito, led by Gonzalo Pizarro, ran short of supplies while exploring east of the Andes in what is today Peru. Pizarros cousin Francisco de Orellana offered to take 60 men along with the boats from the expedition and forage for supplies. De Orellana floated down the Rio Napo to its confluence with the Amazon, near Iquitos (Peru), and then to the mouth of the Amazon. Along the way his expedition suffered numerous attacks by Indians; some of the Indian warriors, they reported, were female, like the Amazons of Greek mythology, and thus the worlds greatest river got its name. No one made a serious effort to claim this sweaty territory, however, until the Portuguese built a fort near the mouth of the river at Belém in 1616, and sent Pedro Teixeira up the river to Quito and back between 1637 and 1639. During the 17th and 18th centuries, Portuguese bandeirantes (groups of roaming adventurers) penetrated ever further into the rain forest in pursuit of gold and Indian slaves, exploring as far as present-day Rondônia, and the Guaporé and Madeira river valleys. Amazonian Indians had long used the sap from rubber trees to make waterproof bags and other items. European explorers recognized the potential value of natural latex, but were unable to market it because it tended to grow soft in the heat, or brittle in the cold, and thus had limited appeal outside the rain forest. However, in 1842 American Charles Goodyear developed vulcanization (made natural rubber durable) and in 1890 Irelands John Dunlop patented pneumatic rubber tires. Soon there was an unquenchable demand for rubber in the recently industrialized USA and Europe, and the price of rubber on international markets soared. As profits skyrocketed, so did exploitation of the seringueiros, or rubber tappers, who were lured into the Amazon, mostly from the drought-stricken northeast, by the promise of prosperity only to be locked into a cruel system of virtual slavery dominated by seringalistas (owners of rubber-bearing forests). Rigged scales, hired guns, widespread illiteracy among the rubber tappers, and monopoly of sales and purchases all combined to perpetuate the workers debt and misery. In addition, seringueiros had to contend with jungle fevers, Indian attacks and all manner of deprivation.
In which year did the fort was built by Portuguese near the river Belem?
The passage consists of six sentences. The first and sixth sentences (S1 and S6) are given. The middle four sentences (P, Q, R, S) are given in jumbled order. Find out the proper order for the four sentences. S1: Most people who have come close to death say they remember nothing. P. It may permanently change a person’s perceptions of what is real and important Q. The near-death experience is among the most powerful experiences that a person can have. R. That ‘something’ might be a near-death experience. S. However, a third or more may later report that ‘something happened.’ S6: However, one extraordinary aspect of near-death experience is that a person’s culture, religion, race or education does not affect the pattern of the experience.
Statement (I) : A monostable multi-vibrator, when switched on remains in a quasi stable state. Statement (II) : Quasi stable state duration is decided by charging time of capacitor. 
Assertion (A): It is desirable that the transient response be sufficiently fast and sufficiently damped. Reason (R): Oscillations are not tolerated in the transient response.
STP-তে একটি আদর্শ গ্যাসকে প্রথমে তার প্রাথমিক আয়তনের এক-তৃতীয়াংশে সংকুচিত করা হয়, এবং তারপর প্রসারিত হতে দেওয়া হয় যতক্ষণ না তার চাপ প্রাথমিক চাপের অর্ধেক হয়। উভয় প্রক্রিয়ায় গ্যাসের তাপমাত্রা স্থির থাকে। যদি গ্যাসের প্রাথমিক অভ্যন্তরীণ শক্তি । হয়ে থাকে তাহলে এর চূড়ান্ত অভ্যন্তরীণ শক্তি কত? (An ideal gas at STP is first compressed to one-third of its initial volume and then allowed to expand until its pressure is half the initial pressure. The temperature of the gas remains constant during both the processes. If the initial internal energy of the gas is U, what is its final internal energy?)