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 non-uniqueness 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.