Unified approach to H_∞-optimal control of singularly perturbed systems: Perfect state measurements

There has been considerable interest in recent literature on the H_∞-optimal control of singularly perturbed systems. Most of this work has been addressed in the continuous-time domain. The key contribution of the current paper is to present continuous and discrete singularly perturbed cases simultaneously from the game theoretic approach, thereby highlighting the similarities and differences. Furthermore, we construct a composite unified controller based on the solution of the slow and fast games, which guarantees a desired achievable performance level for the full-order plant, as the small parameter ε approaches zero. This paper also studies optimality when the controller includes a feedforward term in the disturbance. The unified results given here are valid for both the continuous-time case (sampling interval Δ = 0) and the discrete-time (sampling interval Δ≠0).