I designed a state feedback control with integral action for output tracking applied to a LPV system with 4 scheduling parameters using LMI in MATLAB. The LMI was synthesized upon Lyapunov function. The system dynamics are given by : dx(t)/dt =A(ρ)x(t)+B(ρ)u(t)+E(ρ)d y(t) = Cx(t) x = [x1 x2] the LMI condition is expressed as follows : P(θ) ≥ εI [A_cl(θ) + A_cl(θ)' + 2αP(θ), P(θ)E(ρ); E(ρ)'P(θ), -γI ] ≤ 0 where A_cl(θ) = A_aug(ρ)*P(θ) + B_aug(ρ)*Y(θ) A_aug(ρ) = [A(ρ) zeros(1,2); -C 0] B_aug(ρ) = [B(ρ) 0] P(θ) and Y(θ) are both affine in θ (i.e., P(θ) = P0 + ∑θᵢ*Pᵢ) For many α I tried to solve the LMI but it fails. Any suggestions to overcome this problem? Could you direct me to any other approaches to design the controller?