Further Results on Descriptor Time Delayed System Stability Theory in the sense of Lyapunov: Pandolfi Based Approach

Debeljković, Dragutin Lj.; Stojanović, Sreten B.; Jovanović, Mića; Milinković, S.A.

doi:10.1109/icca.2005.1528144

Cited by 6 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By (8), (15), and (16), it can be shown thatP1 =P T 1 0,P2 = 0. Since matrix P is nonsingular, we conclude thatP1 =P T 1 > 0.…”

Section: Delay-dependent Admissibility Analysismentioning

confidence: 99%

“…Delay is often encountered in various engineering systems, and the existence of delay is frequently a source of instability and poor performances. According to whether they are dependent on delay or not, the controls of singular systems can be classified into two types: delay-dependent control [3, 4, 6, 7, 9, 10, 14−19] and delay-independent control [5,8,18,20] . Generally speaking, delay-dependent results are less conservative than the delay-independent ones, especially when the upper bound of the delay is small.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

Sun

Zhang

Yang

et al. 2010

Int. J. Autom. Comput.

View full text Add to dashboard Cite

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.

show abstract

“…By (8), (15), and (16), it can be shown thatP1 =P T 1 0,P2 = 0. Since matrix P is nonsingular, we conclude thatP1 =P T 1 > 0.…”

Section: Delay-dependent Admissibility Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

Sun

Zhang

Yang

et al. 2010

Int. J. Autom. Comput.

View full text Add to dashboard Cite

show abstract

“…A good review of the literature on all the recent advances on the class of time-delay systems up to 2003 can be find in [24]. Other interesting results on singular systems can be found in [27][28][29][30][31][32][33] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Delay-Dependent Robust Stabilizability of Singular Linear Systems with Delays

Boukas

2009

Stochastic Analysis and Applications

View full text Add to dashboard Cite

This article deals with the class of continuous-time singular uncertain linear systems with time-varying delay in the state vector. The uncertainties we are considering are of norm bounded type. Delay-dependent sufficient conditions on robust stability and robust stabilizability are developed. A design algorithm for a memoryless state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse-free, and robust stable is proposed in terms of the solutions to linear matrix inequalities (LMIs).

show abstract

“…In original paper [25], a crucial mistake was made when solving (3) and using no representative matrix for system stability testing in the corresponding Lyapunov matrix equation. The paper [20] gave an adequate counterexample the basic theorem and it was demonstrated that their statement is incorrect. To eliminate this error, we was proposed a new theorem formulation and showed how to correct the example given there.…”

mentioning

confidence: 99%

Consistency and Lyapunov Stability of Linear Singular Time Delay Systems: A Geometric Approach

Debeljković¹,

Buzurović²,

Simeunović³

2018

Bulletin of the SUSU. MMP

View full text Add to dashboard Cite

When we consider the control design of practical systems (chemical engineering systems, lossless transmission lines, large-scale electric network control, aircraft attitude control, exible arm control of robots, etc.), time-delay often appears in many situations. Singular time delayed systems are the dynamic systems described by a mixture of algebraic and dierential equations with retarded argument. This paper investigates the geometric description of initial conditions that generate smooth solutions to such problems and the construction of the Lyapunov stability theory to bound the rates of decay of such solutions. The new delay dependent conditions for asymptotic stability for the class of systems under consideration were derived. Moreover, the result is expressed in terms of only systems matrices that naturally occur in the model, therefore avoiding the need to introduce algebraic transformations into the statement of the main theorem.

show abstract

Further Results on Descriptor Time Delayed System Stability Theory in the sense of Lyapunov: Pandolfi Based Approach

Cited by 6 publications

References 14 publications

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

Delay-Dependent Robust Stabilizability of Singular Linear Systems with Delays

Consistency and Lyapunov Stability of Linear Singular Time Delay Systems: A Geometric Approach

Contact Info

Product

Resources

About