Chapter 6 State-Space Design
© National Instruments Corporation 6-25 Xmath Control Design Module
Figure 6-7. f and x as a Function of Time, Starting from Zero, as a Result of a Sinusoidal
Force Applied to the System Input
Riccati Equation
Riccati equations, which take one of two distinct forms, arise in a number
of linear systems and controls problems. The best-known use is in the
solution of the optimal regulator and estimator problems, as described
in the Linear Quadratic Regulator section and the Linear Quadratic
Estimator section.
The continuous-time Riccati equation is given by:
The discrete-time Riccati equation is given by:
This function can be used to solve the optimal regulator problem, and by
duality, the optimal estimator problem. An alternative form of the
A′PPA PBS+()inv×R()B′PS′+()Q+–+ 0=
A′PA P A′PB S+()inv R B′PB+()B′PA S′+()Q+×–– 0=