The Rouse Co., the big real estate and shopping mall developer in Columbia, increased its profits 57 percent last year and kicked its dividend up to 72 cents a share from 60 cents a share annually.

Rouse had earnings of $8.1 million (54 cents a share) compared with $5.2 million (37 cents) in 1981. Revenues climbed to $163.6 million from $138.5 million.

Fourth-quarter profits slipped to $2.7 million (19 cents) from $3.1 million (22 cents) in 1981, while revenues increased to $46.5 million from $37.9 million.

Record profits and sales were posted by D.C.-based Systematics General Corp. in its fourth quarter, company officials said, and the information security firm bounced back from the money-losing year it had in 1981.

Fourth-quarter profits grew to $312,000 (22 cents a share) from $23,000 (2 cents), while sales climbed to $4.6 million from $3.1 million.

For the year, Systematics General had earnings of $849,000 (60 cents) compared with a loss of $1.2 million during 1981.

Sales increased to $15.3 million from $12.2 million in 1981. Smithfield Foods Inc., which has corporate offices in Arlington, posted nine-month profits yesterday of $1.3 million (47 cents a share), down from $2.7 million ($1.23) in 1982. More shares were outstanding in 1983 than the year before. Sales jumped to $435.5 million from $226.9 million.

Third-quarter profits fell to $2.9 million (88 cents) from last year's record $3.2 million ($1), while sales grew to $164.1 million from $126.5 million.