Robust positively invariant sets of discrete-time convex polyhedral system family |
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Authors: | Weihua Jiang Lin Huang Tianguang Chu |
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Institution: | (1) Department of Mathematics, Harbin Institute of Technology, 150006 Harbin, China;(2) Department of Mechanics and Engineering Science, Peking University, 100871 Beijing, China |
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Abstract: | Certain problems concerning state constraints and control constraints can often be reduced to the study of positive invariance
of some subsets of the state space of dynamical systems. The robust positive invariance of given linear state constraint sets
of uncertain discretetime systems is studied by the mixed monotone decomposition method. Necessary and sufficient conditions
of the robust positively invariant sets are established for the linear discrete-time system family specified by matrix convex
polyhedron and additive interval disturbances. Also, sufficient conditions are derived for nonlinear system family. All the
conditions are given in terms of the parameters of vertex systems of the system family and are therefore easy to check. Finally,
an illustrating example is given. |
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Keywords: | discrete-time system family robust positively invariant sets mixed monotone decomposition method vertex results |
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