Controllability and Observability

Abstract

This chapter treats the coupling of the input to the state, i.e. controllability, and that of the state to the output, i.e. observability. This is done for general dynamical systems which are then specialized to the linear system representationRO=[A(•),B(•),C(•),D(•)]: first in the time-varying case and then in the time-invariant case. For the latter systems this leads to Kalman decomposition and a discussion of the absence of unstable hidden modes, viz, stabilizability and detectability. This chapter ends with a brief study of 1) balanced representations (based upon normalized controllability and observability grammians) and 2) the robustness of controllability (for perturbed nonlinear systems).