ABSTRACT
The classical methods of studying control systems are mostly referred to single-input–single-output systems, which are described in the time domain by differential equations or by a scalar transfer function in the frequency domain. The modern methods of studying control systems are referred to the general category of multi-input-multi-ouput systems, which are described in the time domain by state equations or by a transfer function matrix in the frequency domain. The concept of controllability is related to the state vector as well as to the output vector of a system. The state-space vector is accordingly decomposed into four subvectors, each one of which corresponds to one of the following four cases: states that are both controllable and observable; states that are uncontrollable but are observable; states that are controllable but unobservable; and states that are both uncontrollable and unobservable.
