Controllability - definition
Controllability - definition
Controllability is a fundamental concept in control theory of dynamic systems, defining the ability of a system to reach any final state from a given initial state in a finite amount of time, using an appropriately chosen control signal. It refers to the intrinsic properties of the system and its response to external forcing, and is one of the key criteria for analysing the controllability and design of control systems.
In mathematical terms, for linear systems described by equations of state, controllability means that the controllability matrix formed from the dynamic equations has a full row, i.e. as many linearly independent rows or columns as the number of state variables. Fulfilment of this condition guarantees that, for each initial configuration of the system, there is such a waveform of the input signal as to guide the system to the desired final state. A lack of controllability indicates that certain states are unattainable or independent of the control signal, which may limit the functionality of the system or require modification.
Controllability is important both in the design of regulators and in stability analysis and optimisation of system performance. In non-linear and discrete systems, the concept retains a similar importance, although its verification may require more complex mathematical tools. In engineering practice, controllability testing assesses whether a control system will be able to fully control the dynamics of a process, which has applications in Industrial Robotics, Aeronautics and Digital Electronics, among others.
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