controllability of LTI systems

Consider the linear time invariant (LTI) system given by:


where A is an n×n matrix, B is an n×m matrix, u is an m×1 vector - called the control or input vector, x is an n×1 vector - called the state vector, and x˙ denotes the time derivative of x.

Definition Of Controllability Matrix For LTI Systems: The controllability matrix of the above LTI system is defined by the pair (A,B) as follows:


Test for Controllability of LTI Systems: The above LTI system (A,B) is controllable if and only if the controllability matrix C(A,B) has rank n; i.e. has n linearly independentMathworldPlanetmath columns.

Title controllability of LTI systems
Canonical name ControllabilityOfLTISystems
Date of creation 2013-03-22 14:32:50
Last modified on 2013-03-22 14:32:50
Owner GeraW (6138)
Last modified by GeraW (6138)
Numerical id 5
Author GeraW (6138)
Entry type Definition
Classification msc 93B05
Defines controllability matrix