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:
“The public history of modern art is the story of conventional people not knowing what they are dealing with.”
—Robert Motherwell (1915–1991)
“The preservation of life seems to be rather a slogan than a genuine goal of the anti-abortion forces; what they want is control. Control over behavior: power over women. Women in the anti-choice movement want to share in male power over women, and do so by denying their own womanhood, their own rights and responsibilities.”
—Ursula K. Le Guin (b. 1929)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)