Modern Control Theory
In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs, outputs and states, the variables are expressed as vectors and the differential and algebraic equations are written in matrix form (the latter only being possible when the dynamical system is linear). The state space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state space representation is not limited to systems with linear components and zero initial conditions. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.
Read more about this topic: Control Theory
Famous quotes containing the words modern, control and/or theory:
“Men must speak English who can write Sanskrit; they must speak a modern language who write, perchance, an ancient and universal one.”
—Henry David Thoreau (18171862)
“Our culture still holds mothers almost exclusively responsible when things go wrong with the kids. Sensing this ultimate accountability, women are understandably reluctant to give up control or veto power. If the finger of blame was eventually going to point in your direction, wouldnt you be?”
—Ron Taffel (20th century)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)