Sorry. Your right. I've just gotten so use of the term "State Space" referring to dx/dt = Ax+Bu y = Cx+Du The example you list above is indeed "state space". However, there are few control design tools for such systems. The majority of the "State Space" control design tools are for linear systems, or nonlinear systems that are constrained to appear linear in some operating region.
Granted you can represent a nonlinear systems using a "state-space" representation and use this representation for simulation. But what "control design tool" do you use that can directly uses this representation for the purpose of design?
I'm trying to think of a nonlinear control design approach that contrasts a linear state space design techniques like H_infinity that uses a linear representation of the plant for the purposes of generating a linear controller.
For things like backlash, and actuator saturation, I would typically do the linear control design for the linear dynamic part of the plant and then wrap this system with logic to handle the specific nonlinearity.....actuactor limit tracking to prevent integrated windup for example.
Think of model predictive control where you take the model (whatever you can afford building), create your optimality functional (where you can penalize excessive actuator movements), impose some certain constrains, create two "horizons" -- one for control and one for model predictions, and run an optimization algorithm to minimize said functional subject to all imposed constrains. It should be noted that tuning and all that of this algorithm is more difficult than the one of PID and the optimizer at the core should be appropriate for the task. However, it is an example of a nonlinear control technique. There are linear versions of MPC, as well. And MPC may work better with PIDs as the baseline control.
Andrey
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