ICARE Implicit solver for continuous-time Riccati equations.
[X,K,L] = ICARE(A,B,Q,R,S,E,G) computes the stabilizing solution X of
the continuous-time algebraic Riccati equation
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A'XE + E'XA + E'XGXE - (E'XB + S) R (B'XE + S') + Q = 0 .
The matrices Q,R,G must be Hermitian and R,E must be invertible. When
omitted or set to [], B,R,S,E,G default to the values B=0, R=I, S=0,
E=I, and G=0. Scalar-valued Q,R,G are interpreted as multiples of the
identity matrix. ICARE also returns the state-feedback gain K and the
closed-loop eigenvalues L given by
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K = R (B'XE + S'), L = EIG(A+G*X*E-B*K,E) .
ICARE returns [] for X,K when there is no finite stabilizing solution.
[X,K,L,INFO] = ICARE(...) also returns a structure INFO with the
following data:
* Vectors SX and SR of state and R scalings
* Basis [U;V;W] of the stable invariant subspace of the associated
scaled matrix pencil
* Diagnostic "Report" with value
0 Accurate solution found (success)
1 Solution accuracy may be poor
2 Solution is not finite
3 Hamiltonian spectrum [L;-L] has eigenvalues on imag. axis.
4 Pencil is singular ([B;S;R] rank deficient)
The solution X and gain K are related to DX=diag(SX), DR=diag(SR), and
U,V,W by
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X = DX V U DX E , K = - DR W U DX .
[...] = ICARE(...,'noscaling') turns off the built-in scaling and
sets all entries of SX and SR to one. This speeds up computation but
can be detrimental to accuracy when A,B,Q,R,S,E,G are poorly scaled.
[...] = ICARE(...,'anti') computes the anti-stabilizing solution X
that puts all eigenvalues of (A+G*X*E-B*K,E) in the right half-plane.
See the reference page for additional algorithmic details.
See also IDARE.
Documentation for icare
doc icare
