Simulation and properties of randomly switched control systems

Power electronics has made great advances since the introduction of the thyristor in 1958. Even a casual study of consumer electronics, such as computer power supplies, reveals that switched mode power electronics have steadily replaced passive circuits. Switched mode circuits can accommodate higher power densities,' they are lighter, cheaper and easier to control. The use of microprocessors and microcontrollers can make switched mode circuits even more versatile. Unfortunately, there are some problems with switched mode circuits. The higher power densities handled by these circuits can cause catastrophic failure. Periodic switching can give rise to acoustic noise2 or undesirable electromagnetic radiation. These problems can be reduced through the use of random switching policies.3 One theoretical disadvantage of random switching policies is that the time averaged switched system is not strictly equivalent to the classical system with the same average parameters. The stability limits for the randomly switched and classical systems are different. This is a possible area for concern, given the high power densities and the possibility of catastrophic failure. In this paper we examine the stability of randomly switched control systems. We provide simulations, some analysis and derive some practical rules for stability. We show that some randomness can beneficial from the point of view of minimising the maximum power spectral density of the noise waveforms in the output current.