Search results
Results from the WOW.Com Content Network
A linear system is BIBO stable if its characteristic polynomial is stable. The denominator is required to be Hurwitz stable if the system is in continuous-time and Schur stable if it is in discrete-time. In practice, stability is determined by applying any one of several stability criteria.
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. [1] [2]In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is
The equilibrium of the above system is said to be exponentially stable if it is asymptotically stable and there exist >, >, > such that if ‖ ‖ < then ‖ ‖ ‖ ‖ for all . Conceptually, the meanings of the above terms are the following:
Because of this recursive structure, the designer can start the design process at the known-stable system and "back out" new controllers that progressively stabilize each outer subsystem. The process terminates when the final external control is reached. Hence, this process is known as backstepping. [3]
In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
Find answers to the latest online sudoku and crossword puzzles that were published in USA TODAY Network's local newspapers.
The relative gain array (RGA) is a classical widely-used [citation needed] method for determining the best input-output pairings for multivariable process control systems. [1] It has many practical open-loop and closed-loop control applications and is relevant to analyzing many fundamental steady-state closed-loop system properties such as ...