Enclosing ellipsoid‐based reachable set estimation for discrete‐time singular systems

Abstract

This article studies reachable set estimation for discrete‐time singular systems. By means of system decomposition and reconstruction, singular systems can be transformed into dynamic systems together with algebraic equations. Under this representation, two novel reachable set estimation methods based on ellipsoidal sets are proposed under nonzero initial conditions. A series of enclosing ellipsoidal sets can be obtained in two derived methods for bounding real‐time states of the considered systems. Finally, the effectiveness of the proposed methods is illustrated with a numerical example.

Hidden Markov model‐based ℋ∞ control for singular Markov jump systems under denial of service attacks

“…Up to date, a lot of basic concepts and theories about SSs, such as stability, stabilization problems, control and filtering problems have been addressed. [1][2][3][4] In parallel, Markov jump systems (MJSs), are commonly used to model some practical systems with abrupt structural and parameter changes, for instance, networked control systems and manufacturing systems. MJSs have attracted a large number of researchers, and many problems, such as stability analysis and robust control problems, have been solved.…”

“…The dynamic behavior of some engineering systems can be better described by SSs than standard state space systems, and typical examples can be found in economic systems, circuit systems, electronic networks, chemical processes, and other fields. Up to date, a lot of basic concepts and theories about SSs, such as stability, stabilization problems, control and filtering problems have been addressed 1–4 . In parallel, Markov jump systems (MJSs), are commonly used to model some practical systems with abrupt structural and parameter changes, for instance, networked control systems and manufacturing systems.…”