Is Kalman Filter for LTV systems applicable on Hybrid systems?

Question

As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But nobody in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of Linear Time Variant (LTV) systems, So my question is why don't people use Kalman Filter for Hybrid systems with linear modes and resort to robust estimation approaches?

Answer 1

You really have two questions -- one, is the Kalman filter applicable to linear hybrid systems, and the other is why isn't it used.

I can't answer your second question.

As for your first question (is it applicable) -- I think it could be made to be applicable. In fact, I strongly suspect that there's some fairly obvious combination of a Kalman-Bucy filter for the continuous-time part of the system and a straight Kalman filter for the discrete-time part.

However

I've found that for a lot of real-world problems involving a discrete-time controller and a continuous-time plant, it's easier to just model the continuous-time plant as a discrete-time system as seen by the controller, optimize the control in discrete time, and then just sweep the fact that the plant is actually continuous time under the rug.

This is because if you're going to make a discrete time controller that actually works in practice, the most reliable way of achieving this end is to make sure that the frequencies of any significant plant dynamics are exceeded by the controller sampling rate by a healthy margin. Do this, and any inaccuracies that you introduce by assuming that the plant responds step-wise to controller commands is less than any inaccuracies from the difference between your best-ever attempt at a plant model and what a real plant is going to do under real circumstances.

However (again)

If you're casting about for a PhD topic, there may be something in here, unless the approach was considered in 1952 and discarded for some good reason.