A Direct Method of Constructing H 2 SuboptimalControllers { Discrete - Time SystemsZongli

For discrete-time systems, an H 2 suboptimal control problem is deened and analyzed. Then an algorithm called`H 2 suboptimal state feedback gain sequence' (H 2 SOSFGS) algorithm is developed. Rather than utilizing a `perturbation method' which is numerically stii and computationally prohibitive, the H 2 SOSFGS algorithm utilizes a direct eigenvalue assignment method to come up with a sequence of H 2 suboptimal state feedback gains. Also, although the sequence of H 2 suboptimal state feedback gains constructed by the H 2 SOSFGS algorithm depends on a parameter ", the construction procedure itself does not require explicitly the value of the parameter ". Next, attention is focused on constructing a sequence of H 2 suboptimal estimator based measurement feedback controllers. Three diierent estimator structures, prediction, current, and reduced order estimators, are considered. For a given H 2 suboptimal state feedback gain, a sequence of estimator gains for any of the three considered estimators can be constructed by merely dualizing the H 2 SOSFGS algorithm. The direct method of constructing H 2 suboptimal controllers developed here has a number of advantages over thèperturbation method', e.g., it has the ability to design all three types of estima-tor based controllers while still maintaining throughout the design the computational simplicity of it. This paper is the discrete-time version of 4]. There are some conceptual similarities as well as fundamental diierences between the H 2 suboptimal control problems for continuous-and discrete-time systems. The fundamental diierences arise mainly from the fact that, in contrast to continuous-time, for discrete-time systems, the innmum of the H 2 norm over the class of strictly proper controllers is in general diierent from the innmum of the H 2 norm over the class of proper controllers.