Research on the H∞ low-order controller parameter sets for discrete time-delay systems

For the discrete-time systems with time delay, the sets of the low-order controller parameters satisfying H_∞ performance are presented by using a simple analytical method. The parameter values in such the sets can not only guarantee the stability of the closed-loop system, but also satisfy the corresponding H_∞ performance. Thus, it can be theoretically proved that there exists a set of the low-order controller parameters satisfying the given H_∞ performance, but not only one group of values. Firstly, we convert the problem of determining the region of the control parameters satisfying H_∞ performance to a closed-loop characteristic polynomial stabilization problem with respect to φ; then, by sweeping over φ (φ ∈ [0,2π)), the boundaries in the control parameters space is calculated for each fixed φ. Thus the stability region of PID parameters for the fixed φ can be determined by examining which side of each boundary has less unstable poles. The region of PID parameters satisfying H_∞ performance is the intersection of these stability regions. The proposed approach provides the theoretical basis for the low-order controller design satisfying multiple performance criteria.