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 Sep8 revised Applied Calculus Homework Question added 3 characters in body Sep8 answered Applied Calculus Homework Question Sep7 answered How to show that a given function is a solution for a partial differential equation. Aug15 answered Weird condition for a transfer function Aug14 answered Solving differential equations with signum Aug10 comment Parametric uncertainty in conditional term of piecewise nonlinear dynamical system The system you're trying to analyze is ridiculously hard to analyze. To make matters worse, you can't even bound the input. Or can you? Maybe some input-to-state stability (ISS) approach would work? Aug10 comment Parametric uncertainty in conditional term of piecewise nonlinear dynamical system What is an acceptable system behavior? Are you talking about the actual mechanical system, or its mathematical model? Aug10 revised What exactly is Laplace transform? edited body Aug10 awarded Supporter Aug10 awarded Editor Aug10 awarded Teacher Aug10 comment What exactly is Laplace transform? Then think of the LT as a tool that simplifies the analysis of RLC circuits and mass-spring systems. The LT not only gives you the solutions of ODEs, it also helps you design a circuit / mechanical system such that it has some desired properties. In other words, the LT is useful not only for analysis, but also for synthesis. Aug10 revised What exactly is Laplace transform? added 74 characters in body Aug10 answered What exactly is Laplace transform? Aug10 comment Parametric uncertainty in conditional term of piecewise nonlinear dynamical system What is your exact goal? You already have a model. You can simulate it in Simulink if you want. But, what is your question? Do you want to know if the system is globally asymptotically stable (under some conditions) for all values of $\delta$ in some interval? Since you have a CT-PWA system, closed-form solutions are kind of out of question, and analytical results will likely be very hard to find. Maybe you can discretize the system in time? Discrete-time PWA systems are actually easier to analyze. Aug10 answered Parametric uncertainty in conditional term of piecewise nonlinear dynamical system