Switched system observability

This thesis investigates conditions for observability of hybrid switched systems. Hybrid switched systems consist of a set of continuous-time state dynamical behaviors (termed vector fields) chosen according to some underlying automata or decision making process. Specifically the vector fields, which determine the derivative of the state vector, switch according an underlying decision or control process. The dynamics determined by each vector field is called a mode of operation. Unlike classical state observability, hybrid system observability entails both mode and state observation. This thesis begins by reviewing linear state model observability and then rigorously developing the existing results for switched linear state models. Necessary and sufficient conditions for observability are presented for switched linear state models when the switching sequence and the state are unknown. This approach is extended to distinguishing sets of modes in the later part of the thesis. The central results of the thesis present an alternate approach to observability of switched systems having nonlinear vector fields. This approach uses the Hadamard\u27s Global Inverse Theorem which expands local observability conditions used in classical nonlinear observability. Sufficient conditions for observability of nonlinear switched systems are developed, proven, and exemplified