Give a definition of an equilibrium of a hybrid automaton.
Give definitions of (uniform) stability, (global uniform) asymptotic stability, and (global uniform) exponential stability of a hybrid automaton.
Does stability of the continuous dynamics at each individual discrete state (mode, location) guarantee stability of the full hybrid automaton?
Does instability of the continuous dynamics at some of the discrete state (mode, location) prevent the full hybrid automaton from being stable?
Give conditions of (uniform) asymptotic stability of a hybrid automaton in terms of Lyapunov-like functions.
Explain the essence and the pros and the cons of a common Lyapunov function (CLF) approach to stability analysis.
Explain the common quadratic Lyapunov function (CQLF) approach to stability analysis.
Restricting to a hybrid automaton with linear dynamics in each mode, formulate the problem of finding a CQLF as a linear matrix inequality.
Explain the S-procedure and show how it can be used to formulate the problem of a piecewise quadratic Lyapunov function?
Skills (use the knowledge to solve a problem)
Analyze stability of a switched linear system under arbitrary switching by formulating and solving (using a computer) the relevant linear matrix inequalities (LMI).
Analyze stability of a switched linear system using a piecewise quadratic Lyapunov function.