ABSTRACT
Any multivariable linear time invariant (LTI) system is uniquely described by its impulse response matrix. The Laplace transform of this matrix function of time gives rise to the system’s transfer function matrix (TFM). We assume that all systems in the sequel have TFM representations; frequency response analysis is always applied to TFM descriptions of systems. For the case of finite dimensional LTI systems, when we have a state-space description of the system, closed-form evaluation of the TFM is particularly easy. This is discussed in Example 8.1. More generally, infinite-dimensional LTI systems also have TFM representations, although closed-form evaluation of the TFM of these systems is less straightforward. Stability (in whatever sense) is presumed; without stability we cannot talk about the steady-state response of a system to sinusoidal inputs. For such systems, the TFM can be measured by means of sinusoidal inputs. We will not discuss the use of frequency-domain techniques in robustness analysis.
