Optimal controller synthesis with multiple objectives

We present a methodology to address the general multiobjective (GMO) control problem involving the ℓ₁ norm, H₂ norm, H_∞ norm and time-domain constraint (TDC). We show that the problem resulted from imposing a regularizing condition always admits an optimal solution, and suboptimal solutions with performance arbitrarily close to the optimal cost can be obtained by constructing two sequences of finite dimensional convex optimization problems whose objective values converge to the optimum from below and above. A numerical example is presented to illustrate the effectiveness of the proposed methodology.