On the decomposition of state space

The response of a linear control system is often viewed as a superposition of independent, modal responses. For complex systems, traditional techniques for resolving modal responses may be either inapplicable, quite expensive, or numerically unstable. A new method, which incorporates the
QR
transformation with several properties of matrix equations, is proposed here as an alternative. The method effectively decomposes a system into a set of independent subsystems having the same natural frequencies as the original system.