Modern control theory

Usually, when speaking about the “modern” automatic control, we think of that part of the control theory that relies on the state-space approach to system representation and design. This approach is particularly important for the systems with multiple inputs and outputs and for the higher-order systems in general. The “classical” control, characterized by the use of frequency domain methods, is still preferable for lower-order single-input single-output systems. Although the adjective “classical” may suggest that this approach is a matter of the past, it is certainly not. In many cases the most effective attack on a problem is made by a combined use of both frequency and state-space methods. That shouldn’t be surprising, because, as T. Kailath says in [22], transfer functions (or high-order differential equation) descriptions and state-space (or first-order differential equation) descriptions are only two extremes of a whole spectrum of possible descriptions of finite-dimensional systems.