Pax Americana is dead. We have entered a post-American world.

Too hasty? Well, according to the Economist magazine the American President is no longer the world's most powerful leader. That mantle belongs to China's Xi Jinping.

It is Xi who talks about being the champion of globalisation and international trade, while Donald Trump's mantra is "America first".

At risk is a global order imagined by Woodrow Wilson, the US president during World War I: democracy, capitalism, interventionism, that laid a platform for economic growth, innovation and human rights.

Political scientist Joseph Nye saw this future more than a decade ago when he published The Paradox of American Power.

Writing after the September 11 terror attack, Mr Nye warned about the dangers of American complacency.

The US changed its gaze

After the collapse of the Soviet empire and the end of the Cold War, Nye said the United States stopped paying attention to the world and turned their sights inward.

Even those who did look beyond America, he wrote, "became arrogant about our power, arguing that we did not need to heed other nations. We seemed both invincible and invulnerable".

Tragically Osama bin Laden reminded America just how vulnerable it was.

Fast forward and America is rubbing up against the limits of its power.

Barack Obama talked a good game but what did his presidency actually achieve? ( NPG )

War and recession have left it weary.

The Obama years began with a theme of hope. Remember his victory speech? "This was the moment when the rise of the oceans began to slow and our planet began to heal."

His critics called it the "Moses speech".

Eight years later, those same critics declared the Obama presidency a failure.

Even in the sober-minded journal Foreign Affairs, Harvard University's Professor of International Relations, Stephen Walt, said it was, "a tragedy, especially when it comes to foreign policy".

Obama's gone, but Kim, Assad and Putin remain

There is a cased to be made that Mr Obama was a poor foreign policy president.

Yes, he got bin Laden. But he was accused of poorly handling the war in Afghanistan, unnecessarily prolonging a conflict that today has failed to oust the Taliban.

Mr Obama underestimated the rise of Islamic State, declaring it a "JV" (junior varsity) terrorist organisation.

He misread the Arab Spring, failing to see the threat of violent extremists who had exploited the upheaval.

He demanded Syria's President, Bashar al-Assad, "must go", drawing red lines about the use of chemical weapons then failing to enforce them.

Mr Assad is still there, with Russian backing that has allowed Vladimir Putin to impose his power on the region.

Mr Obama failed to deliver on his pledge of a two-state solution between Israelis and Palestinians.

Under Mr Obama, North Korea entrenched its status as a nuclear-armed state.

Mr Obama told the Australian Parliament America was "all in" in the Asia-Pacific, but his so-called pivot to Asia has done nothing to curb China's growing power and influence.

The United States has been the predominant power in our region since the end of World War II, yet China has been able to reclaim and militarise disputed islands in the South China Sea, raising fears of igniting a wider conflict.

China represents a new model of power: economic liberalism and political control.

Xi is part of a global return of the political strongman.

China has been part of a return of big-power politics.

As political commentator Robert Kagan wrote in The Return of History and The End of Dreams: "Today, a new configuration of power is reshaping the international order."

In Easternisation: War and Peace in the Asian Century, journalist Gideon Rachman argues the West, more broadly, is in decline and Asia is filling the void.

"The political, strategic and ideological dominance of the West is now under challenge," he writes.

Donald Trump is either trashing or rebuilding America's reputation, depending where you stand. ( Reuters: Jonathan Ernst )

Wielded well, US power helps many

Enter Donald Trump.

Mr Trump came to power rejecting multilateral trade deals, talking protectionism, banning migrants and building walls.

He has questioned US military pacts and accused allies of freeloading.

It must make Joseph Nye nervous. In The Paradox of American Power he warned: "Our desire to go it alone may ultimately weaken us."

But at the Davos global leaders meeting, Trump may have softened, America first, he said, does not mean America alone.

Mr Trump has shown how mercurial he can be, but taken at his word a more capacious American leadership is a good sign.

It would be far too premature to count America out.

Mr Trump may not be as popular with much of the world as he is with his supporters, but that doesn't mean the world does not need him. ( Reuters: Ringo Chiu )

The United States is still the world's superpower, with the biggest economy and the most powerful military. It has enormous "soft power": the world watches its movies, listens to its music, carries its phones, works on its computers and wears its fashion.

American power has rightly been criticised at times as morally dubious and selective. It has been guilty of over reach and misadventure with disastrous consequences: The world is still dealing with the loss of life and upheaval from the war in Iraq.

But the history of the past half-century reminds us that American power, exercised effectively, is crucial.

It is American-backed regional security that has helped underwrite the rise of China.

Europe's idea of a post-nation future, has been possible because of its American security alliance.

As Mr Kagan wrote: "American power made it possible for Europeans to believe that power was no longer important."

Mr Trump may not be popular with much of the world, but that doesn't mean the world does not need him.

Right now, as he delivers his inaugural state of the union speech, he has an opportunity to remind the world just how important American power remains.

Matter of Fact is on the ABC News Channel at 9pm, Monday to Thursday.