Annie Lennox sings a lot about despair, but her soaring range and vocal control at Royce Hall give the impression of hope.

Annie Lennox’s old partner in Eurythmics, Dave Stewart, once described the Scottish-born singer by saying, “There is exaltation and there is misery, and nothing much in between.”

Maybe so, but Lennox’s ability to mix those emotional extremes in her music has made her one of the most commanding figures in pop -- and she was at her liberating best on Tuesday at UCLA’s Royce Hall.

The performance, one of the final stops on Lennox’s first solo tour, was a terrific piece of theater and an inspiring salute to the survival instinct in us all.

Misery certainly appears to fuel Lennox as a songwriter. In many of her songs, she describes troubled relationships in images that go beyond gray skies and broken hearts to an inner tension so deeply rooted that she tells us “dying is the easy part, it’s the living that scares me.” In one song, she dubs herself the “queen of doom.”

Exaltation, on the other hand, radiates in Lennox’s vocals, arrangements and stage manner. It’s as if she confronts the confusion and despair in the songs, then slays the demons with music that is hopeful and healing.

The whole package hit with triumphant force Tuesday as Lennox, bristling with confidence and authority, had the cheering audience on its feet so often you’d have thought they were delegates at a political convention on candidate nomination night.

With Eurythmics in the ‘80s, Lennox and Stewart made some splendid pop hits, including “Sweet Dreams (Are Made of This), “ “Missionary Man,” “Who’s That Girl?” and “Here Comes the Rain Again.” But there was so much emphasis on sonic dynamics -- especially a relentless synthesizer pulse -- and theatrical images, including her gender-bending Bowie-ish look, that Eurythmics’ success sometimes felt based more on cleverness and pop strategy than on any particular songwriting depth.

On her own since 1990, Lennox has blossomed into a more complete artist -- one of the few, including Don Henley and Sting, who has challenged herself in a solo role rather than merely recycling the elements that brought initial success in rock.

Lennox still has a great sense of visual style. She moves about the stage with a performance artist’s purpose and flair, often underscoring a lyric marvelously with just a sudden glance over her shoulder or a sweep of the arm across her bowed head. She has such long, lean legs that she sometimes seems like she’s walking on stilts as she takes sudden, dramatic steps, while acting out the drama of a tune.

Her songs, meanwhile, explore relationships with more daring than before, and the arrangements draw nicely from R&B;, rock, pop and even touches of cabaret to provide a more distinctive and soulful edge.

Lennox’s singing, too, is more tailored, with even her most ordinary songs taking on greater weight as she gives each word its own thoughtful interpretation without ever seeming self-conscious.

Her reworkings of several Eurythmics hits, including a version of “Here Comes the Rain Again” with her at the piano, also brought added emotional fiber to the numbers. Lennox’s range is wide enough to be equally effective on the R&B-fused; sisterhood celebration “Sisters Are Doin’ It for Themselves” and a brooding rendition of Neil Young’s “Don’t Let It Bring You Down.”

But the evening’s most powerful moment was tied to a song from Lennox’s new album, which is titled “Bare” and due in June. The collection was written after the breakup in 2000 of her 12-year marriage to filmmaker Uri Fruchtman, and the songs are typically despondent.

One, “Pavement Cracks,” summarizes the liberating side of her music as eloquently as anything she has done.

Dressed almost totally in black at Royce Hall, Lennox stood motionless at the microphone and delivered the song’s opening lines in a near whisper about how the sky is its usual gray and how all her water colors have turned to black.

“I’m going nowhere and I’m 10 steps back / All my dreams are fading fast.”

The tight, five-piece band then kicked in with a brighter, infectious pulse that eventually led to a point where Lennox and three female backup singers turned the number into a foot-stomping, neo-gospel workout that lifted your spirits with almost irresistible force

At the end, however, Lennox returned to a whisper, as if saying, “Dare we really dream again?”

The fact that she can manage to find the strength to consistently answer that question in the affirmative is what gives Lennox’s music its ultimate power.

In a pop world where artists often have a short shelf life, Lennox is showing that, at 48, she is just entering her creative prime. It’s hard to imagine what kept her this long from embarking on a solo tour, but now that she’s here, she carries a knockout punch.