It's an intriguing idea, but I can't see that the analogy holds true. Booms and crises are better seen as excessive fluctuations than anything heading towards infinity and excessive fluctuations exist in control systems as well, especially if there's time-lags involved.
And in any case, dosn't every transaction involve people with different beliefs? The seller bets that his money can be spent better elsewhere and the buyer bets that the same amount is best spent on the stock, so they must have different beliefs about where it or other stocks are heading?
The same goes for short-selling, where you'r betting against someone and the short-selling may actually produce extra financial instruments so that even short-selling indirectly fuels the race of those that think the stock prices will rise.
Still, it seems to make sense at least to try framing the stock market in terms of control theory. Has anyone come across better expositions in this direction?