Lazareva E. The Structural Analysis and Optimization Multirate Continuous-Discrete Control Systems

Thesis is devoted to search the decision of several tasks in a field of multirate automatic control systems widely used in engineering and industry. A continuous-discrete-time state-space description is derived for multivariable multirate sampled-data systems. The suggested models provide the high adequacy in comparison with existing time-area models. Based on obtained result, stability criterion is derived. Analysis algorithms of structural properties (controllability, observability and stabilizability) of continuous-discrete control systems are offered and theoretically proved. A new optimal multirate design of linear continuous-time time-invariant systems is considered. It is based on solving the LQR problem with the control being constrained to a certain piecewise constant feedback. А multirate scheme provides a powerful design method for computer-based control of continuous-time systems. Necessary and sufficient conditions for asymptotic stability of the resulting closed-loop system are given. Anexplicit multirate feedback law requires the solution of an algebraic discrete Riccati equation is presented. Examples are given to illustrate the main points.