zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Delay-dependent criterion for guaranteed cost control of neutral delay systems. (English) Zbl 1070.93039

The author considers a system described by a neutral functional differential equation

x ˙(t)-Cx ˙(t-τ)=A 0 x(t)+A 1 x(t-h)+Bu(t)

with (A 0 +A 1 ,B) a controllable pair. To this system he associates the quadratic cost function

J(u,φ)= 0 (x T (t)Qx(t)+u T (t)Su(t))dt

where Q>0, S>0 and φC 1 is the initial condition. The paper aims to find a control law u(t)=-B T Px(t) such that the resulting closed-loop system is exponentially stable with guaranteed quadratic cost JJ * , where J * >0 is some number. The paper relies on the choice of a quadratic Lyapunov functional leading finally to some Linear Matrix Inequalities whose feasibility guarantees the problem’s solution.

MSC:
93D15Stabilization of systems by feedback
34K40Neutral functional-differential equations
93C23Systems governed by functional-differential equations
93D30Scalar and vector Lyapunov functions
15A39Linear inequalities of matrices
References:
[1]
[2]
[3]
[4]
[5]
[6] · Zbl 0814.65078 · doi:10.1007/BF01935649
[7] · Zbl 0669.34074 · doi:10.1017/S0004972700027684
[8] · Zbl 0878.34063 · doi:10.1016/0096-3003(95)00301-0
[9] · Zbl 0969.34066 · doi:10.1016/S0016-0032(98)00040-4
[10] · Zbl 0947.65088 · doi:10.1023/A:1021781602182
[11]Ni, B., and Han, Q., On Stability for a Class of Neutral Delay-Differential Systems, Proceeding of the American Control Conference, Arlington, Virginia, pp. 4544-4549, 2001.
[12] · Zbl 1060.34043 · doi:10.1023/A:1016087332235
[13]Park, J. H., Robust Stability of a Class of Uncertain Linear Neutral Systems with Time-Varying Delay, Journal of Systems Analysis Modeling Simulation, Vol. 43, pp. 741–748, 2003.
[14]
[15] · Zbl 0849.93055 · doi:10.1109/9.489272
[16] · Zbl 0807.93054 · doi:10.1080/00207179408923147
[17] · Zbl 0822.93057 · doi:10.1007/BF02192121
[18] · Zbl 0259.93018 · doi:10.1109/TAC.1972.1100037
[19] · Zbl 1041.93530 · doi:10.1016/S0005-1098(99)00007-2
[20] · Zbl 0976.93059 · doi:10.1006/jmaa.2000.7040
[21]
[22]Gu, K., An Integral Inequality in the Stability Problem of Time-Delay Systems, Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805-2810, 2000.
[23]