Direct method of constructing H₂-suboptimal controllers: Continuous-time systems

An H₂-suboptimal control problem is defined and analyzed. Then, an algorithm called H₂-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a direct eigenvalue assignment method to come up with a sequence of H₂-suboptimal state feedback gains. Also, although the sequence of H₂-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ε, the construction procedure itself does not require explicitly the value of the parameter ε. Next, attention is focused on constructing a sequence of H₂-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H₂-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The direct method of constructing H₂-suboptimal controllers developed here has a number of advantages over the perturbation method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.