Robust control analysis and design for discrete-time singular systems
Citations
759 citations
Cites background from "Robust control analysis and design ..."
...It should be pointed out that the robust stability problem for singular systems is much more complicated than that for regular systems because it requires to consider not only stability robustness, but also regularity and absence of impulses (for continuous singular systems) and causality (for discrete-singular systems) at the same time [6], [7], and the latter two need not be considered in regular systems....
[...]
324 citations
105 citations
Cites background or methods from "Robust control analysis and design ..."
...is a known positive integer time delay of the system, and are highly structured matrices representing time-invariant parameter uncertainties, and are assumed to have the following properties [ 7 ], [12]:...
[...]
...Both results in [6] and [ 7 ] can be viewed as extensions of those for state‐space systems....
[...]
...When parametric uncertainties appear, the problems of robust D-stability analysis and robust D-pole placement for discrete-time singular systems have been investigated in [ 7 ], and sufficient conditions have been obtained....
[...]
...It is worth pointing out that the robust D-stability problem for singular systems is much more complicated than that for state‐space systems because it requires to consider not only D-stability robustness, but also regularity and impulse immunity (for continuous singular systems) and causality (for discrete singular systems) simultaneously [6], [ 7 ], while for state‐space systems, the latter two issues do not arise....
[...]
100 citations
78 citations
References
9,334 citations
4,017 citations
Additional excerpts
...(Chen, 1984, Theorem 3-4)....
[...]
1,315 citations
"Robust control analysis and design ..." refers background or methods in this paper
...Sometimes the system is called generalized state-space systems, or implicit systems, or descriptor systems or semistate systems (Lewis, 1986)....
[...]
...The system Ex(k + 1) = Ax(k) is said to be asymptotically stable if and only if (Lewis, 1986):...
[...]
...INTRODUCTION In the past ten years, there has been a growing interest in the system-theoretic problems of singular systems due to the extensive applications of singular systems to large-scale systems, circuits, economics, polynomial matrices and other areas (Luenberger, 1977; Verghese et al., 1981; Lewis, 1986; Dai, 1989; Fang and Chang, 1991, 1992)....
[...]
...The system Ex(k + 1) = Ax(k) is said to be asymptotically stable if and only if (Lewis, 1986): all roots of IzE - AI = 0 lie inside the disk D(0, 1)....
[...]
...By the Weierstrass decomposition (Dai, 1989; Lewis, 1986), we propose a simple method to evaluate the matrix T without performing the expansion of ( z E -...
[...]
1,042 citations
"Robust control analysis and design ..." refers background in this paper
...…growing interest in the system-theoretic problems of singular systems due to the extensive applications of singular systems to large-scale systems, circuits, economics, polynomial matrices and other areas (Luenberger, 1977; Verghese et al., 1981; Lewis, 1986; Dai, 1989; Fang and Chang, 1991, 1992)....
[...]
...We only assume the triple (E, A, B) is strongly controllable (Verghese et al., 1981)....
[...]
...INTRODUCTION In the past ten years, there has been a growing interest in the system-theoretic problems of singular systems due to the extensive applications of singular systems to large-scale systems, circuits, economics, polynomial matrices and other areas (Luenberger, 1977; Verghese et al., 1981; Lewis, 1986; Dai, 1989; Fang and Chang, 1991, 1992)....
[...]
...It has been known that a singular system generally contains three kinds of modes: dynamical finite modes, dynamical infinite modes, and nondynamical infinite modes (Verghese et al., 1981; Bender and Laub, 1987)....
[...]