In this paper the problem of designing a single actuator control for a class of systems is addressed. The existence of such control is studied and several ways for designing such control are provided. The results depend either on the rational canonical form or on the Jordan structure associated with the matrix which characterizes the system dynamics. The constructed control laws can be employed...

We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions {Ci(P ) : P ∈ Q[x], i = 0, . . . , deg(P )} defined by Ci(P )(x) = { 0 if x ≤ α P (x) if x ≥ α where α is the i-th real root of the polynomial P . These functions will allow us to represent and manipul...

Matrix-geometric distributions (MG) and discrete (time) rational arrival processes (DRAP) are natural extensions of discrete phasetype distributions (DPH) and discrete Markov arrival processes (DMAP) respectively. However, the exact relation of the Markovian classes and their non-Markovian counterparts and the boundaries of these classes are not known yet. It has been shown that for the order t...

Many linear macroeconomic models can be cast in the …rst-order form, AEtyt+1 = Byt +CEtxt; if the matrix A is permitted to be singular. For this singular linear di¤erence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinental polynomial jAz ¡ Bj is not zero for some value of z, and (ii) a rank condition is satis…ed which is a ...

From the definition of the "terms" of a phrase, it is clear that if a phrase is free of parentheses all its terms are letters. Hence, by II , any phrase-equation E whose members are free of parentheses is interderivable with any phrase-equation resulting from permutation of non-initial letters within members of E. Therefore any phrase-equation whose members are free of parentheses and have like...

Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational or relevant closure according to the (propositional) KLM postulates. If in DDLs with quantification a defeasible subsumption relationship holds between concepts, this relationship might also hold if these concepts appear in existential restrictions. Such ne...