The observer-controller design study for linear continuous-time systems with norm-bounded uncertainties is tackled using a finite frequency method. More precisely, the study uses the Generalized Lemma of Kalman Yakobovich Popov (GKYP) to develop conditions over finite frequency ranges, formulated into Linear Matrix Inequalities (LMIs), to design a controller in one step method. The provided conditions reduce the conservatism factor by optimizing the uncertainties' performance. At the end of the paper, a comparative study is given through an example of illustration to highlight the effectiveness of the suggested approach.