1. stable and controllable
2. stable but uncontrollable
3. unstable but controllable
4. unstable and uncontrollable

Given : ẋ = Ax + Bu ;

A =		-1			2		, B =		0
		0			2				1

For stability, characteristic equation

∴ M = (s + 1) × (s – 2) = 0
⇒ (s – 2) (s + 1) = 0
⇒ s = 2, s = – 1
So one root in right hand side of s-plane, so system is unstable.

For controllability : B =		0
		1

AB =		-1			2				0		=		2
		0			2				1				2

= 0 – 2 = – 2 ≠ 0
So controllable.

The system ẋ = Ax + Bu with A =		-1			2		, B =		0		is
		0			2				1