Reachability and observability of linear impulsive systems

Observability criteria for impulsive control systems with applications to biomedical engineering processes

“…Note that x(·), and g(·) depend on x 0 and u i . , g(x) = B, and f I (x) = A I x, this system is a linear ICS and can be expressed as (Medina & Lawrence, 2008) …”

“…The state transition matrix of (8) is calculated recursively using (7) and Medina & Lawrence, 2008 for more details). The state response of system (8) on [0, t] with k impulses applied to the system is…”

“…Observability in linear ICS has been investigated in Guan, Qian, and Yu (2002), Medina and Lawrence (2008), Shi and Xie (2012) and Xie and Wang (2005). The definition used therein establishes that observability depends on measurements of the output on a finite-time interval [0, t f ].…”

A geometric approach for reachability and observability of linear switched impulsive systems

“…[9,10,12,13]. Geometric analysis of reachability and observability generally includes the construction of the reachable and observable set in terms of invariant subspaces and investigation of the properties of the reachable and observable subspaces [22,26,27].…”

“…Moreover, it is well known that the issue of controllability and observability plays an important role in the control theory and engineering [7][8][9][10][11][12][13][14][15]. There has been some research dealing with the controllability and observability issues for impulsive systems due to its theoretical and practical significance via algebraic method [16,17], fixed-point theorem [18][19][20] and geometric analysis [21][22][23].…”