Worst-case topological entropy and minimal data rate for state observation of switched linear systems

We introduce and study the concept of worst-case topological entropy of switched linear systems under arbitrary switching. It is shown that this quantity is equal to the minimal data rate (number of bits per second) required for the state observation of the switched linear system with any switching signal. A computable closed-form expression is presented for the worst-case topological entropy of switched linear systems. Finally, a practical coder-decoder, operating at a data rate arbitrarily close to the worst-case topological entropy, is described.