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SIAN EDWARDS will become the first woman to conduct an opera at the Royal Opera House, Covent Garden, when she makes her debut at Britain's leading opera house on April 29. The Royal Opera said she would conduct a new production of Sir Michael Tippett's ``The Knot Garden,'' with the composer attending the performance. Edwards has already conducted opera at Glyndbourne and in Scotland. She will open the 1989-90 season with Verdi's ``Rigoletto.'' LINDA ELLERBEE will be featured in a TV series to start next January under the banner of Hearst Broadcasting Productions, a joint venture of King Features Entertainment and the six Hearst TV stations. Each program will feature news, film clips, features, and interviews bearing the Ellerbee stamp. MICHAEL JACKSON was named Best International Solo Artist at the sixth annual British Phonographic Industry awards, Britain's equivalent of the Grammy awards. Jackson's album ``Bad'' was Britain's best-selling LP of 1987. THE ACTORS THEATRE OF LOUISVILLE will perform in the US Information Agency's ``American Theatre Today'' exhibit in Warsaw during March and April. ATL's productions include ``Cervelles aux Beurre Noire,'' by festival producing director Jon Jory; ``Fifteen Minutes,'' ``Handler,'' and ``Travelin' Show,'' by Jane Martin; ``Cheek to Cheek,'' by John Pielmeier; and ``Groves of Academe,'' by Mark Stein.