New delay-dependent criteria for stability and stabilization of uncertain singular systems with time delay

A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay

“…the delay is time invariant. The maximum allowed τ, obtained by the criteria in 3, 5–8, 10–13, 15, 35, 37 and Corollary 4.1 of this paper, is shown in Table I. The numerical results shown in Table I illustrate that the stability criterion in Corollary 4.1 gives higher upper bound on the delay than 3, 5, 6, 11–13, 37, and has same upper bound with 7, 8, 10, 15, 35, 36.…”

“…The maximum allowed , obtained by the criteria in [3, 5-8, 10-13, 15, 35, 37] and Corollary 4.1 of this paper, is shown in Table I. The numerical results shown in Table I illustrate that the stability criterion in Corollary 4.1 gives higher upper bound on the delay than [3,5,6,[11][12][13]37], and has same upper bound with [7,8,10,15,35,36]. On the other hand, the stability criterion in Corollary 4.1 when L = 0 involves fewer number of variables than those in [3, 6, 10-13, 15, 35], and has the same number of variables with those in [7,8,37].…”

“…For given scalars d and satisfying (2), the singular LPV system (5) is said to be robustly stable if for any >0 there exists a scalar ( )>0 such that, for any compatible initial function (t) satisfying sup − t 0 (t) ( ), the solution x(t) to (5) satisfies that x(t) for any t 0, and x(t) → 0 as t → ∞ for any satisfying (3) and (4).…”

Improved Stability and Stabilization Criteria of Singular System with Time-delay and Parameter Uncertainties

“…Hence, the study of delay-dependent stability for singular time-delay systems has received increasing attention. In terms of LMI approach, several delay-dependent stability criteria were given in [9,10,11,12]. [9,10] investigated the delay-dependent robust stabilization problem for uncertain singular time-delay systems by using model transformation and bounding technique for cross-terms.…”

“…[9,10] investigated the delay-dependent robust stabilization problem for uncertain singular time-delay systems by using model transformation and bounding technique for cross-terms. [11,12] also discussed the problem, and neither model transformation nor bounding technique for cross-terms is needed in the development of the results. By employing the delay decomposition approach, [13] established a delay-dependent criterion for singular time-delay systems to be regular, impulse free and asymptotically stable.…”