The Brics economies have been hit by falling global demand and lower commodity prices, while some have faced corruption scandals.
Brazil and Russia are both in recession, and Brazil on some counts is suffering its worst downturn since the 1930s.
South Africa narrowly avoided a recession last month, while China is going through its slowest economic growth in 25 years.
Still, Lord Jim O'Neill, the economist who coined the term "Brics", told the BBC he remained confident of the grouping's success.
Ahead of the talks, he said it is "bigger today [than] even in the most optimistic scenario I thought 15 years ago, and it's primarily because of China".
'Asian century'
At the summit, the Brics leaders agreed to set up a new credit rating agency and expand the role of emerging economies, and recognised the threat from terrorism.
In separate agreements, Mr Xi vowed to pursue closer ties with India and Russia as part of a wider Chinese push to foster global trade partnerships.
Indian Prime Minister Narendra Modi said India and China had a responsibility to join hands and turn the 21st Century into an Asian century.
Meanwhile, Mr Modi and Russian President Vladimir Putin signed multi-billion dollar energy and defence pacts on Saturday on the sidelines of the summit.

“Alibaba is a company aiming to help solve social problems. In 20 years, we hope to serve two billion consumers around the world, empower 10 million profitable businesses and create 100 million jobs,” wrote Ma in the annual letter to shareholders, stressing that the group would be in for an even more difficult journey than the one it has gone through.

Ma expects three more decades of fast technological change across industries. The change will include transformation of traditional retailers in a multi-trillion dollar market.

“Throughout history, technological disruptions have followed similar trajectories: 20 years of technological disruption followed by 30 years of further rapid change as new technologies are applied throughout society,” the letter says.

Alibaba aims to invite retailers to join its system of online selling platforms, advertising tools as well as cloud computing offerings.

“We are working to create the fundamental digital and physical infrastructure for the future of commerce, which includes marketplaces, payments, logistics, cloud computing, big data and a host of other fields,” the CEO wrote, adding that the company didn’t try to switch transactions from offline to online.

The budget for 2016 predicted $50 oil, $10 above the average price in the first nine months of the year. And once again, the government was forced to change its plans.
It amended the budget earlier this month, to accommodate higher defense spending and a one-off bonus for pensioners to be paid in January. That will push up borrowing: the budget deficit is now expected to reach 3.7% of GDP, well above the official target of 3%.
The government is now expecting the deficit to fall to slightly above 3% of GDP next year.
Prime Minister Dmitry Medvedev said on Thursday Russia cannot afford to continue living in debt, and ordered more spending cuts. He wants the deficit to be less than 1.2% of GDP by 2019.
But Putin is up for election in 2018 in the middle of the budget cycle, and that will limit the scope for spending cuts or tax increases, said Anna Zadornova, an economist with UBS.
putin russia reserves

Russia desperately needs to get its finances in order, because its cash reserves are being depleted at a rapid rate. Analysts expect the country's rainy day fund will shrink to just $15 billion by the end of this year and dry up completely soon after that. It was $91.7 billion in September 2014, just before oil prices started to collapse.
Experts are skeptical whether the country will be able to stick with the plan. "Russia's inability to stick to a fiscal plan even over the course of several months undermines the spending and deficit targets for 2017 and beyond," analysts from the Eurasia Group wrote in a note.
Russia is trying to become less dependent on oil and gas. Energy now accounts for 37% of all government revenues, compared to roughly 50% just two years ago.
Eurasia Group analysts say the government is still opting for more austerity rather than genuine economic reform.

Volkswagen and General Motors, which have wrangled with Toyota for the top spot in sales volume, both seem to see scale as only a secondary focus going forward. They are actively pouring resources into such advanced technologies as artificial intelligence to cultivate ride-hailing and other services.

VW actually has a history of partnering with Suzuki. The two formed a capital partnership back in 2009, when Ferdinand Piech was still in charge. But the German carmaker's strong focus on capitalist logic hurt the relationship, and the tie-up ended in September 2015. Dashed were VW's hopes of borrowing Suzuki's know-how in developing small vehicles for such emerging markets as India.

Heading off a crisis

Now, under a new chief, VW has set its sights on something different. Matthias Mueller took the helm after the diesel emissions scandal and has said since day one that the company should not pursue scale alone. A key part of its strategy through 2025 is to become the global leader in mobility services. The automaker expects minimal growth in annual sales volume over the nine years from the current 10 million units.

VW invested in Israeli ride-hailing company Gett in May, making Uber Technologies of the U.S. a rival in the automaker's eyes. Mueller sees a future in which many people stop owning cars. This sense of urgency is driving the shift in business models.

Adding new brands was like a hobby for Piech. In contrast, the 13th brand Mueller announced at the Paris Motor Show in September was for car-sharing and on-demand services -- targeting those who do not own cars. In effect, VW is creating a new playing field to steer clear of the Toyota-Suzuki juggernaut.

GM is also moving to cultivate new business by tapping the latest technologies. It announced in January a $500 million investment in ride-hailing company Lyft. And in March, GM said it would buy a Silicon Valley startup developing self-driving systems. The American automaker thus acquires software engineers and other talent it cannot cultivate in-house. GM will begin tests of self-driving taxis with Lyft as early as this year.

Toyota and Suzuki had thrived on their ability to slash costs. In the West, automakers are increasingly handing these efforts over to fast-growing manufacturing services providers. In Europe, some such companies even develop engines. Automakers have freed up internal resources to instead plow into self-driving technologies and next-generation powertrains, for example.