A system is described by the state equationx1̇ = 2

A system is described by the state equation
x₁̇ = 2 0 x₁ + 1 u
x₂̇ 0 2 x₂ 1

The state transition matrix of the system is

Here , A =		2			0
		0			2

The state transition matrix of the system.
φ (t) = £^{– 1} (sI – A)^{– 1}

[sI - A] =		s			0		-		2			0
		0			s				0			2

=		(s - 2)			0
		0			(s - 2)

[sI - A]^{– 1} =	1		(s - 2)			0
[sI - A]^{– 1} =	(s - 2)²		0			(s - 2)

=		e^2t			0
=		1			e^2t

	x₁̇		=		2			0			x₁		+		1		u
	x₂̇				0			2			x₂				1

	e^-2t			0
	0			e^-t

	e^-2t			1
	1			e^-t