In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm

Constrained control for uncertain discrete-time linear systems / Benvenuti, Luca; Farina, Lorenzo. - In: INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL. - ISSN 1049-8923. - 8(1998), pp. 555-565. [10.1002/(SICI)1099-1239(199806)8:7<555::AID-RNC329>3.0.CO;2-S]

Constrained control for uncertain discrete-time linear systems

BENVENUTI, Luca;FARINA, Lorenzo
1998

Abstract

In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/247936
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