Analysis and synthesis of time-varying systems via orthogonal hybrid functions (HF) in state space environment

This paper uses a set of hybrid functions (HF) formed by a combination of sample-and-hold function (SHF) set and triangular function (TF) set. The SHF set has been applied for analysing sample-and-hold control systems and the TF set has been proved to be efficient for obtaining piecewise linear solutions of control systems. In the present work, the HF set has been employed for the analysis and synthesis of homogeneous as well as non-homogeneous time-varying control systems in state space. The HF set works with function samples, and is thus useful for building an easier algorithm for time-varying system analysis. After developing necessary theories, a few examples are treated to illustrate the efficiency as well as simplicity of the approach. The results thus obtained are compared with the results obtained via traditional analysis, and relevant tables and graphs are included to justify the case for hybrid functions.