Closed-loop control system robustness improvement by a parameterised state feedback

State feedback is one of the most popular and well known techniques for altering the transient response of a closed-loop system. This technique is usually used to assign the eigenvalues of a closed-loop system to desired locations under the assumption of complete controllability. In the case of multi-input systems, the feedback gain matrix permitting the assignment of a desired set of eigenvalues is nonunique and, hence, different gain matrices can be used. This nonuniqueness of the gain matrix offers extra degrees of freedom that permit the designers not only to place the closed-loop system eigenvalues but also to satisfy some performance indices beyond the eigenvalues assignment problem. One important performance measure is the closed-loop system robustness to parameter variations or to external disturbances. Closed-loop system robustness is often a major concern of control designers, since design is usually based on nominal values of system parameters which are rarely those of normal operations. This paper considers closed-loop system robustness to two types of system deviations from nominal or ideal design conditions