System analysis and design using consolidity theory with applications

This paper is directed towards confirming the important role of the consolidity index in the analysis and design of real life systems. Consolidity is an internal property of systems that plays an essential role in governing their parameters changes when subjected to events or varying environments “on and above” their normal operations or original set points. For this purpose the paper is divided into two parts: the analysis and the design. The analysis part we check how the consolidity index is used for appropriate choice of parameters which are selected arbitrarily before. The analysis verification part is demonstrated by solving the problem of selecting the arbitrary matrix in Lyapunov equation for deriving the required stability conditions and also the Kalman Riccati matrix in solving Linear Quadratic Regulation problem based on the consolidity theory. In design part, some free parameters are permitted in the system to obtain the best compromise among system pillars (stability, controllability, and consolidity). As an illustration, two examples of the disk drive system and the national economy system are given to demonstrate how to attain such best compromise. Finally, the attained results confirm the importance of incorporation of the system consolidity as an essential tool in both system analysis and design.