ABSTRACT
The dynamics of biological systems are generally highly nonlinear — what then is the justification for using linear control system analysis techniques to study such systems? The answer to this question will be familiar to any engineering undergraduate, since it is a fact that while almost all real-world control systems display nonlinear dynamics to some extent, the vast majority of the methods used in their design and analysis are based on linear systems theory, from the flight control system on the Airbus A380 to the controller for the servomotor which accesses the hard disk on your computer. Essentially, we have a trade-off: control engineers will, in certain cases, accept the level of approximation involved in modelling the process as a linear system in order to exploit the power, elegance and simplicity of linear analysis and design methods. The key point to remember is that when we model or analyse the dynamics of a particular system we are usually interested only in certain aspects of that system’s dynamics — if these may be approximated to a reasonable level of accuracy as a linear system, then there are huge advantages in doing so. The only caveat is that we then need to be careful in interpreting the results of our analysis, as these will hold only within the limitations of the underlying assumptions regarding linearity.
