| The Focus of this research has been to design feedback controllers for linear shift-invariant discrete two-time-scale systems. The theory of singular perturbation is utilized to split the full system (high dimension) into two reduced-order subsystems. Therefore, the approach was to design controllers for these lower-order subsystems, then the composition of these controllers was fed back to asymptotically stabilize the closed-loop system. A pair of nonsingular transformation matrices are used to decouple the multivariable system. Several mathematical models of two-time-scale sampled-data control systems are studied. Structural properties of the system are established in terms of those of the slow and fast subsystems. State feedback, observer-based controller, and optimal state feedback design with quadratic cost functional problems are solved. Some of these designs were bases on standard and some nonstandard singularly perturbed systems. Application of the theory developed is demonstrated by two examples; first, the longitudinal dynamics of an aircraft and second, a fifth order steam power system. |
