### Citations

392 |
Linear Optimal Control Systems
- Kwakernaak, Sivan
- 1972
(Show Context)
Citation Context ...lemma's in section II, we treat target point problems in section m. Although these problems were treated before (see e.g. Meditch [14] th.2.2 and th.2.4,sLudyck [13] th.2.2 and th.2.4, and Kwakernaak =-=[11]-=- th.6.7.), either the solutions there weresincomplete, or the proofs were false. So for completeness sake we give here results for controllability, stabilizability, output and reachability problems, t... |

195 |
On the Theory of Economic Policy.
- Tinbergen
- 1952
(Show Context)
Citation Context ...e (strong) admissibility of a target path.sI. IntroductionsExactly tracking a target path has attracked a lot of attention both in control theory andseconomics.sAfter the pioneering work of Tinbergen =-=[21]-=-, Brockett and Mesarovic [5] formulated necessarysand sufficient conditions for target path controllability in linear continuous time-invariant systems.sSince then a lot of papers appeared on this sub... |

55 |
The theory of matrices second edition.
- Lancaster, Tismenetsky
- 1985
(Show Context)
Citation Context ... Proof:sFollows directly from the equality v (k) = e (k + 1) - A (k) e (k) . osThe second lemma gives necessary and sufficient conditions for solvability of a linear equation.sA proof can be found in =-=[12]-=-, chap. 3.10.sLemma 2:sLet B be an n x m matrix.sThen the equation B u = y is solvable if and only if (iff) rank [B I y] :: rank B. Moreover, thessolution is uniquely detennined iff rank B = m. Then t... |

45 |
Almost invariant subspaces: an approach to high gain feedback design - Part II: Almost conditionally invariant subspaces
- Willems
- 1981
(Show Context)
Citation Context ... time-invariant systems we call attention to two algorithms developed for time-invariant systems which bear a great similarity withsour algorithm.sOne of them is the algorithm developed by Willems in =-=[24]-=-, see also [23] for an extension. toscalculate the controllable L..,-almost output nulling subspace. The difference between this algorithm and the one developed here is the initialization. Our algorit... |

34 |
Decoupling in the Design and Synthesis of Multivariable Control Systems,"
- Falb, Wolovich
- 1967
(Show Context)
Citation Context ... + p + q) not diagonal. To solve this problem, we have to consider the decoupling problem first.sThe decoupling problem, as defined here, was solved for time-invariant systems by Falb andsWolovich in =-=[8]-=-. A first attempt to generalize this result to time-varying systems was taken bysPorter in [15]. In this paper a sufficient condition for the so called integrator decoupling problem was given. This pr... |

10 |
Pagan: The theory of economic policy.
- Preston
- 1982
(Show Context)
Citation Context ...cked for a period of length k.sSubsequent questions concern the maximum of such numbers k and the reaction time, i.e. thestime needed to reach the target path (also known as policy lead question). In =-=[16,25]-=- this problem was solved for time-invariant systems. Here we derive an algebraic algorithm for timevarying systems. This section is followed by a section in which the decoupling problem iss- 2 - solve... |

8 |
A geometric approach to the singular filtering problem",
- Schumacher
- 1986
(Show Context)
Citation Context ...vantage of the last algorithm is that the subspace Siscan be interpreted as:sSi = {x E X I 3 W E Si-1> U E U such that A (I + i - 2) w + B (I + i - 2) U = x andse(t + i-I) w = OJ (see e.g. Schumacher =-=[20]-=-).sFor the derivation of results concerning global TPC is the following lemma imponantsLemma 10:sLet .'E be time-invariant.sIf the lead p is greater than n, then for all i ;:: 2 is IR, C lRi-l .s- 20 ... |

6 |
Decoupling of and Inverses for Time-Varying Linear Systems,’’
- Porter
- 1969
(Show Context)
Citation Context ...t.sThe decoupling problem, as defined here, was solved for time-invariant systems by Falb andsWolovich in [8]. A first attempt to generalize this result to time-varying systems was taken bysPorter in =-=[15]-=-. In this paper a sufficient condition for the so called integrator decoupling problem was given. This problem deals with the question under which conditions compensatorssF (k) and G (k) exists such t... |

4 |
Sufficient conditions for control of target variables and assignment of instruments in dynamic macroeconomic models
- Aoki, Canzoneri
- 1979
(Show Context)
Citation Context ...oint in time on is more interesting. This question has therefore gained a lot of attention in economics. People who weresengaged in this subject are e.g. Tinbergen [21], Preston and Sieper [17], Aoki =-=[3,4]-=-. Prestonsand Pagan [16] and Wohltmann [26]. The contribution of this paper is among others thatsresults are generalized to time-varying systems.sFollowing Wohltmann [26] especially two questions are ... |

2 | Path controllability of linear input-output systems - Albrecht, Grasse, et al. - 1986 |

2 | A dynamic generalization of Tinbergen's theory of policy - AJ - 1974 |

2 |
Singular optimal control, a geometric approach
- Kitai, Silverman
(Show Context)
Citation Context ... systems we call attention to two algorithms developed for time-invariant systems which bear a great similarity withsour algorithm.sOne of them is the algorithm developed by Willems in [24], see also =-=[23]-=- for an extension. toscalculate the controllable L..,-almost output nulling subspace. The difference between this algorithm and the one developed here is the initialization. Our algorithm in general s... |

2 |
Target path controllability of linear time-varying dynamical systems
- Wohltmann
- 1985
(Show Context)
Citation Context ...cessarysand sufficient conditions for target path controllability in linear continuous time-invariant systems.sSince then a lot of papers appeared on this subject [1,3.4,16-19,25].sRecently Wohltmann =-=[27]-=- and Grasse [9] extended the results to continuous time-varying systems.sThis paper is concerned with discrete time-varying systems. After introducing some notationsand establishing some elementary le... |

1 |
On a generalization of Tinbergen's condition in the theory of policy to dynamic models; Review of Economic Studies vol.42
- AoId
- 1975
(Show Context)
Citation Context ...oint in time on is more interesting. This question has therefore gained a lot of attention in economics. People who weresengaged in this subject are e.g. Tinbergen [21], Preston and Sieper [17], Aoki =-=[3,4]-=-. Prestonsand Pagan [16] and Wohltmann [26]. The contribution of this paper is among others thatsresults are generalized to time-varying systems.sFollowing Wohltmann [26] especially two questions are ... |

1 |
The solution of the infinite time reference trajectory tracking problem for discrete-time systems possessing an exogenous component; Memorandum Cosor 86-08
- lC
- 1986
(Show Context)
Citation Context ...y too.s"¢:::" By making use again of the structure of the error equation matrix as derived above thisspart is easily proved. 0sWe conclude this section with an illustration of theorem 10.sIn Engwerda =-=[7]-=-, the infinite time quadratic tracking problem was solved under some conditions. As a special case the following problem was treated:sN-lsmin lim L {(y(k)-y*(k)l Q(y(k)-y*(k» + (u(k)-u*(k)lR (u(k)-u*(... |

1 |
Time~Variant Discrete-Time Systems
- Ludyck
- 1969
(Show Context)
Citation Context ...ationsand establishing some elementary lemma's in section II, we treat target point problems in section m. Although these problems were treated before (see e.g. Meditch [14] th.2.2 and th.2.4,sLudyck =-=[13]-=- th.2.2 and th.2.4, and Kwakernaak [11] th.6.7.), either the solutions there weresincomplete, or the proofs were false. So for completeness sake we give here results for controllability, stabilizabili... |

1 |
Policy objectives and instrumental requirements for a dynamic theory of policy
- Sieper
- 1977
(Show Context)
Citation Context ...specified point in time on is more interesting. This question has therefore gained a lot of attention in economics. People who weresengaged in this subject are e.g. Tinbergen [21], Preston and Sieper =-=[17]-=-, Aoki [3,4]. Prestonsand Pagan [16] and Wohltmann [26]. The contribution of this paper is among others thatsresults are generalized to time-varying systems.sFollowing Wohltmann [26] especially two qu... |

1 | Massey 1.L., Invertibility of linear time-invariant dynamical systems - Sain - 1969 |

1 |
On the decoupling of linear time-varying control systems
- Tzafestas, Pimenides
- 1976
(Show Context)
Citation Context ...hat the closed loop system (D y )(t) ;:: A (t) w (t) tel!. results. HeresA is a diagonal matrix, and D is an operator which is defined below. This result was generalized by Tzafestas and Pimenides in =-=[22]-=-.sDue to the decoupled inputs influencing the outputs succeeding (D y)(1) and which can not bescontrolled by u(t + 1), a solution to the integrator decoupling problem solves in general not thesdecoupl... |

1 |
Dictaat Systeemtheorie, lecture notes course 1980 chap.4
- lC
(Show Context)
Citation Context ...cked for a period of length k.sSubsequent questions concern the maximum of such numbers k and the reaction time, i.e. thestime needed to reach the target path (also known as policy lead question). In =-=[16,25]-=- this problem was solved for time-invariant systems. Here we derive an algebraic algorithm for timevarying systems. This section is followed by a section in which the decoupling problem iss- 2 - solve... |

1 |
maximal controllability of discrete economic systems
- Wohltmann, Complete
- 1981
(Show Context)
Citation Context ...estion has therefore gained a lot of attention in economics. People who weresengaged in this subject are e.g. Tinbergen [21], Preston and Sieper [17], Aoki [3,4]. Prestonsand Pagan [16] and Wohltmann =-=[26]-=-. The contribution of this paper is among others thatsresults are generalized to time-varying systems.sFollowing Wohltmann [26] especially two questions are discussed: how long is the minimumspolicy l... |