The concept of entropy was initially put forward in thermodynamics as a measure of the degree of disorder in a thermodynamic system. Thereafter various kinds of entropies appeared in different areas. This thesis is mainly concerned with the topological entropy of a continuous-time LTI system. It measures the uncertainty that an observer has on the system state. We further argue that the topological entropy can be interpreted as a measure of instability of a system. Three application problems are comprehensively studied to justify this argument....[ Read more ]

The concept of entropy was initially put forward in thermodynamics as a measure of the degree of disorder in a thermodynamic system. Thereafter various kinds of entropies appeared in different areas. This thesis is mainly concerned with the topological entropy of a continuous-time LTI system. It measures the uncertainty that an observer has on the system state. We further argue that the topological entropy can be interpreted as a measure of instability of a system. Three application problems are comprehensively studied to justify this argument.

We first study the minimum energy control problem for a continuous-time multi-input LTI system. By solving a special LQR problem, we show that the minimum energy for stabilization equals twice the topological entropy of the plant. Then we study the stabilization problem of the multirate networked control systems with information constraints in the input channels. By the lifting technique and the resource allocation method, we show that a multirate networked control system could be stabilized by state feedback if and only if the overall channel capacity is larger than the topological entropy of the plant. Finally, we investigate the mean square stabilization problem of a continuous-time LTI system over a stochastic network. An encouraging result is obtained that the feedback system can be stabilized in the mean square sense if and only if the mean square capacity of the network is larger than the topological entropy of the plant. All these studies provide us compelling evidence to support the interpretation of the topological entropy as a measure of instability.