×

zbMATH — the first resource for mathematics

On invariant polyhedra of continuous-time systems subject to additive disturbances. (English) Zbl 0851.93046
Summary: This paper presents new necessary and sufficient algebraic conditions on the existence of positively \({\mathcal D}\)-invariant polyhedra of continuous-time linear systems subject to additive disturbances. In particular, for a convex unbounded polyhedron containing the origin in its interior, it is also shown that the positive \({\mathcal D}\)-invariance conditions can be split into two lower-dimensional sets of algebraic relations: the first corresponds to disturbance decoupling conditions and the second to positive \({\mathcal D}\)-invariance conditions for bounded polyhedra of a reduced-order system. The stability of the overall system is discussed as well. By exploring the results obtained, a linear programming approach is proposed for solving a state-constrained regulator problem in the presence of additive disturbances.

MSC:
93C73 Perturbations in control/observation systems
93D09 Robust stability
90C05 Linear programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bitsoris, G., Existence of polyhedral positively invariant sets for continuous-time systems, Control—theory adv. technol, 7, 407-427, (1991)
[2] Blanchini, F., Feedback control for linear time-invariant systems with state and control bounds in the presence of disturbances, IEEE trans. autom. control, AC-35, 1231-1234, (1990) · Zbl 0721.93036
[3] Carvalho, A.N.; Milani, B.E.A., A simple design method for robust linear discrete-time regulators under symmetrical constraints, (), 778-781
[4] Castelan, E.B.; Hennet, J.C., Eigenstructure assignment for state constrained linear continuous-time systems, Automatica, 28, 605-611, (1992) · Zbl 0766.93048
[5] Castelan, E.B.; Henet, J.C., On invariant polyhedra of continuous-time linear systems, IEEE trans. autom. control, AC-38, 1680-1685, (1993) · Zbl 0790.93099
[6] Dórea, C.E.T.; Milani, B.E.A., A computational method for optimal L-Q regulation with simultaneous disturbance decoupling, Automatica, 31, 155-160, (1995) · Zbl 0825.93248
[7] Fletcher, R., Constrained optimization, () · Zbl 0322.90053
[8] Linnemann, A., A condensed form for disturbance decoupling with simultaneous pole placement using state feedback, (), 92-97
[9] Porter, B., Eigenvalue assignment in linear multivariable systems by output feedback, Int. J. control, 25, 483-490, (1977) · Zbl 0347.93018
[10] Schneider, H.; Vidyasagar, M., Cross-positive matrices, SIAM J. numer. anal., 7, 508-519, (1970) · Zbl 0245.15008
[11] Tarbouriech, S.; Burgat, C., Positively invariant sets for constrained continuous-time systems with cone properties, IEEE trans. autom. control, AC-39, 401-405, (1994) · Zbl 0800.93778
[12] Wonham, W.M., ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.