Synthesis of discrete systems: certain nonstandard problems (Q1883856)

In the synthesis of systems with a square criterion, higher quality can be achieved by additional procedures. This is discussed for several cases. (1) Stabilization of the output of a static system with additive noise: The constraints of the system characteristics are investigated. It is shown that a control strategy exists under certain conditions which enables the almost sure convergence of the control. (2) Synthesis of a linear stabilization controller with deterministic disturbances: Given a minimum-phase system with a specific transfer function of the controller, a stabilization controller is designed which ensures a limited output variance. The role of the definition of the disturbance spectral density is discussed. Furthermore, an extension to certain nonminimal-phase systems is presented. (3) The similar case but with special restrictions in the spectral domain (constrained transmission band): A stabilizing controller exists with given suboptimality level. Summarizing, the results show that the quality which can be reached strongly depends on the given constraints.