Unified ${maths\cr H}_\infty$ Control to Suppress Vertices of Plant Input and Output Sensitivity Functions

This note presents a discrete-time H_∞ controller to attenuate effects of external disturbances introduced from both plant input and plant output. In this note, two stage control structure is constructed so that state variable dependent conventional controllers and H_∞ loop shaping controllers are simultaneously utilized, which is a different approach from previous methods. For the loop shaping controller, a new weighting function derived from an open loop transfer function of fictitious state-feedback systems is proposed. Since the weighting function inherits implicit stability margins, sufficiently stable closed loop systems are designed, therefore well damped transient responses are achieved.