Analysis and Synthesis of Homogeneous / Non-Homogeneous Control Systems via Orthogonal Hybrid Functions (HF) under State Space Environment

Abstract

The present work uses a new set of hybrid functions (HF) formed by the synthesis of sample-and-hold functions (SHF) and triangular functions (TF). The SHF set is efficient for analyzing sample-and-hold control systems and the TF set have been employed for obtaining piecewise linear solution of control problems. After a brief review of the basic theory of HF, the operational matrices for integration in HF domain are also briefly discussed. Finally, this HF set is employed for the analysis and synthesis of homogeneous and non-homogeneous systems described via state space. Many examples are treated and the results are compared with the exact solutions and found to be attractively close. Since the HF set works with function samples, the computational burden in the presented method are much less than traditional ones.