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Solve discrete-time Lyapunov equations
X = dlyap(A,Q)
X = dlyap(A,B,C)
X = dlyap(A,Q,[],E)
X = dlyap(A,Q) solves the discrete-time Lyapunov equation AXA^{T} − X + Q = 0,
where A and Q are n-by-n matrices.
The solution X is symmetric when Q is symmetric, and positive definite when Q is positive definite and A has all its eigenvalues inside the unit disk.
X = dlyap(A,B,C) solves the Sylvester equation AXB – X + C = 0,
where A, B, and C must have compatible dimensions but need not be square.
X = dlyap(A,Q,[],E) solves the generalized discrete-time Lyapunov equation AXA^{T} – EXE^{T} + Q = 0,
where Q is a symmetric matrix. The empty square brackets, [], are mandatory. If you place any values inside them, the function will error out.
The discrete-time Lyapunov equation has a (unique) solution if the eigenvalues α_{1}, α_{2}, …, α_{N} of A satisfy α_{i}α_{j} ≠ 1 for all (i, j).
If this condition is violated, dlyap produces the error message
Solution does not exist or is not unique.
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