StateFeedbackGains

StateFeedbackGains[ssm,{p₁,p₂,…,p_n}]

gives the state feedback gain matrix for the state-space model ssm, such that the poles of the closed-loop system are p_i.

StateFeedbackGains[{ssm,{in₁,…}},…]

specifies control inputs in_i to use.

Details and Options

StateFeedbackGains is also known as pole placement gains.
The state-space model ssm can be given as StateSpaceModel[{a,b,…}], where a and b represent the state and input matrices in either a continuous-time or a discrete-time system:
continuous-time system

discrete-time system
If ssm is controllable, the eigenvalues of will be {p₁,p₂,…,p_n}, where is the computed state feedback gain matrix.
For a descriptor system StateSpaceModel[{a, b, c, d, e}] the number of poles that can be specified is determined by the rank of e and the controllability of the system.
StateFeedbackGains also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
For nonlinear systems, the operating values of state and input variables are taken into consideration, and the gains are computed based on the approximate Taylor linearization and returned as a vector.
StateFeedbackGains[{ssm,{in₁,…}},…] is equivalent to StateFeedbackGains[ssm₁,…], where ssm₁SystemsModelExtract[ssm,{in₁,…}].
StateFeedbackGains accepts a Method option with settings given by:
Automatic automatic method selection

"Ackermann" Ackermann method

"KNVD" Kautsky–Nichols–Van Dooren method