Your use case is similar to a
hidden-markov-model (HMM) but not quite since your state names are known and your training data is already labelled.
Based on your labelled dataset, you can learn not only the transition matrix between states (stable/unstable) but also the observation probabilities per state. In other words, given [speed1=3, speed2=2, Pressure=1, acceleration=0.7], are you more likely to be in a stable or unstable state? You learn this based on MLE on your labelled set.
Then, when it comes to labelling the unlabelled series, you know your initial state probabilities (stable / unstable), your [2*2] transition matrix and the observations (and therefore likely state) at each time point.
Since you have multiple observed features (emissions), you can implement something similar to a Dynamic Naive Bayes solution, which is a generalisation over HMM's. Or you can use an HMM and model your emission as a multivariate Gaussian.
You can then run a Viterbi algorithm to find the best sequence of states. You can start with looking at
Rubiner, HMM paper.
There are implementations of HMM in R, Matlab, Python, etc. I am sure you will find these easily upon Googling.