A descriptor approach to singular LQG control programmes using Wiener-Hopf methods : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Production Technology at Massey University
Wiener-Hopf methods are used in this thesis to solve the output feedback Linear
Quadratic Gaussian (LQG) control problem for continuous, linear time-invariant
systems where the weighting on the control inputs and the measurement noise intensity
may be singular. Some outstanding issues regarding the closed loop stability of WienerHopf
solutions and its connection with partial fraction expansion are resolved.
The main tools in this study are state-space representations and Linear Matrix
Inequalities. The relationship between Linear Matrix Inequalities and Wiener-Hopf
solutions is studied; the role of the Linear Matrix Inequality in determining spectral
factors, the partial fraction expansion step, the form of the controller, and the value of
the performance index is demonstrated.
One of the main contributions of this thesis is the derivation of some new descriptor
forms for singular LQG controllers which depend on the solution to the Linear Matrix
Inequalities. These forms are used to establish the separation theorem for singular LQG
control problems and to investigate the order of singular LQG controllers.