The non-symmetric discrete algebraic Riccati equation and canonical factorization of rational matrix functions on the unit circle.

Canonical factorization of a rational matrix function on the unit circle is described explicitly in terms of a stabilizing solution of a discrete algebraic Riccati equation using a special state space representation of the symbol. The corresponding Riccati difference equation is also discussed. © The Author(s)

Macro Control Languages And Actions For Cocolog

. The control of a discrete event system is specified in the COCOLOG logic control system by use of an extra-logical representation of the control laws in terms of Conditional Control Rules (CCRs); these are conditionaction pairs in which the conditions are mutually exclusive and exhaustive formulas in the language (L k ) at the instant k, k 0. Such formulas are tested for deducibility from \Sigma k , the current COCOLOG axiom set, and once the unique deducible formula is found, the associated control action is applied to the system. The simplicity of L k leads to even the most basic concepts having a complex expression as well formed formulas in L k . Furthermore, the triggering of elementary control actions often depends upon complex nested sets of Conditional Control Formulas (CCFs) expressed in L k . In response to this set of problems, this article presents the foundations for (i) a theory of the expression of complex predicates and functions in terms of simple Macro COCOLOG Lang..