Hybridní systémy

I know it and understand it

• 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.

I can use it 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).