State feedback stabilization of linear time-varying systems on time scales

Davis, John M.; Gravagne, Ian; Jackson, Billy; Marks, Robert J.

doi:10.1109/ssst.2010.5442794

Cited by 8 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, s. Sincek i = Kv i , the last inequality is equivalent to Kv i < a i . Thus there must exist K that satisfies (11), so the set of these inequalities is consistent.…”

Section: Stabilizationmentioning

confidence: 99%

See 1 more Smart Citation

Stability and stabilization of linear positive systems on time scales

Bartosiewicz

2020

Positivity

View full text Add to dashboard Cite

show abstract

“…, s. Sincek i = Kv i , the last inequality is equivalent to Kv i < a i . Thus there must exist K that satisfies (11), so the set of these inequalities is consistent.…”

Section: Stabilizationmentioning

confidence: 99%

“…We rely here on [3] and [4], where uniform exponential stability of linear systems was studied. Stability of linear systems on time scales was also considered in [5,6,7,8,9,10,11,12,13,14]. Various authors considered different concepts of stability and different variants of the same concept.…”

Section: Introductionmentioning

confidence: 99%

Stability and stabilization of linear positive systems on time scales

Bartosiewicz

2020

Positivity

View full text Add to dashboard Cite

show abstract

“…This appendix is reproduced from the authors' previous works as convenience to readers not yet familiar with the theory of time scales [5]. The theory of time scales springs from the 1988 doctoral dissertation of Stefan Hilger [11] that resulted in his seminal paper [10].…”

Section: Appendix: Dynamic Equations On Time Scales a What Are Timentioning

confidence: 99%

Switched linear systems on time scales with relaxed commutativity constraints

Gravagne

Johns

Davis

2011

2011 IEEE 43rd Southeastern Symposium on System Theory

Self Cite

View full text Add to dashboard Cite

Abstract-A fundamental stability result for arbitrarily switched linear systems in continuous time assumes that the set of system coefficient matrices are commutative with one an other. This result was recently generalized to include arbitrarily switched linear system on arbitrary time scales T, with additional constraints imposed upon the graininess of the time scales. In the following analysis we explore the case when pairs of switched systems are noncommutative by visualizing the space of common Lyapunov solutions graphically. We deduce that there are cases in which a common Lyapunov solution exists for a noncommutative switched system if the time scale graininess is limited to some upper bound 1 .

show abstract

“…Time scales is introduced as a PhD thesis by Stefan Hilger in 1988 which unifies continuous and discrete time systems. Recently, time scales has gained attention in control theory (Jackson et al [2009], Pawluszewicz and Bartosiewicz [2005], , Davis et al [2009b], Davis et al [2010], Bartosiewicz and Pawiuszewicz [2004], Sevim and Goren-Sumer [2012]). In computer controlled systems, constant sampling periods may not be achieved due to some practical problems like jitter, computational delays, communication delays, etc.…”

Section: Introductionmentioning

confidence: 99%