AbstractThis article proposes a hybrid search (involving the performance level and a positive scalar variable in sequence) based method for synthesis of linear time‐invariant (LTI) static output feedback (SOF) controllers for a class of linear systems with norm‐bounded time‐varying parametric uncertainties. Using an available extended linear matrix inequality (LMI) formulation of bounded real lemma, a new sufficient condition in terms of LMIs is obtained for existence of SOF controllers, where a triangular structure in the variable part of the Lyapunov matrix is introduced, unlike the diagonal structure existing in direct synthesis methods in literature. To obtain as less as possible, the part of the Lyapunov matrix which is kept fixed while computing the variable part is first obtained using a ‐search based method. Then with this fixed part, the final variable triangular part of the Lyapunov matrix is obtained using a single positive scalar search based LMI method to further reduce . The efficacy of the proposed method is studied on a number of benchmark examples. The method is also extended for structured SOF design. Finally, the proposed method is applied to design two‐degree‐of‐freedom (2‐DOF) multivariable proportional‐integral‐derivative (PID) controllers for compensation of norm‐bounded uncertain plants. A case study on designing roll–pitch–yaw integrated missile autopilots is also considered to show the efficacy of the proposed multivariable PID compensation.