State space 8 - similarity transformations

State  space models are not unique in that one can get models with equivalent  input/output behaviour but very different state definitions. This resources  introduces the concept of equivalence and shows how one can from state space  models with a desirable structure. Readers are reminded that changing the model  structure and changing the states may mean there is no longer a physical  interpretation for the model states. Also  looks at transformation possible using an eigenvalue/vector decomposition which  exposes the underlying behaviours as being linked to the eigenvalues.

Lectures aimed at engineering undergraduates. Presentation focuses on understanding key prinicples, processes and problem solving rather than mathematical rigour.

• #education
• #rossiter
• #analysis
• #control
• #laplace
• #modelling
• #behaviour
• #engineering_education
• #feedback
• #state_space
• #transition_matrix
• #eigenvalues
• #eigenvectors
• #eigenmodes
• #step_response
• #poles
• #phase_plane
• #decay
• #similarity_transform
• #canonical_forms
• #matlab
• #transfer_function_from_state_space
• #state_space_from_transfer_function
• #discrete_state_space