Time-domain analysis of power and energy dynamics of MIMO systems

Signals by themselves are not sufficient to analyze and design control systems with optimum and robust performance. In this paper, analysis and design problems are formulated in terms of basic physical quantities such as power and energy. First, the author develops a general framework to analyze the power and energy dynamics of multivariable systems. The power and energy interactions between various input-output nodes are investigated by using tensor products and the Kronecker algebra. In particular, tensor differential equations that describe instantaneous power and energy dynamics of MIMO systems are derived. Closed-form analytical solutions of the power differential equations are presented for systems without any external inputs