Positive Invariance for Linear Sampled-data Systems

Abstract: The sampled-data framework captures conventional sampled-data systems, and it also provides an adequate representational tool for contemporary cyber-physical and smart autonomous systems. One of the major concerns for analysis and synthesis of such systems is safe operation under constraints. This paper contributes to resolving this cornerstone aspect by focusing on related positive invariance notions within sampled-data setting. More specifically, we introduce generalized positive invariance notions that are topologically compatible with sampled-data framework and that overcome inevitable conservatism of the classical positive invariance notions. We propose exact generalized positive invariance and complement it with the guaranteed generalized positive invariance. The former notion is topologically nonconservative, while the latter notion is approximate and guaranteed but it leads to finitely parameterizable and practically computable generalized positively invariant sets. The limiting behaviour and computational aspects are also discussed, and an example illustrating the proposed notions is provided. Keywords:. Positive Invariance, Constrained Systems, Linear Sampled-data Dynamical Systems. Positive Invariance, Constrained Systems, Linear Sampled-data Dynamical Systems