Uncertain Singular Time-delay Systems Research Articles

Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems

In this note, the delay-dependent robust stability criteria for two classes of singular time-delay systems with norm-bounded uncertainties are investigated. First, without using model transformation and bounding technique for cross terms, an improved delay-dependent stability criterion for the nominal singular time-delay system is established in terms of strict linear matrix inequalities (LMIs). Then, based on this criterion, the delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems are proposed, which ensure that the systems are regular, impulse free and asymptotically stable for all admissible uncertainties. Numerical examples are proposed to illustrate the less conservatism of the obtained results

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time-delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities (LMIs) involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.

DELAY‐DEPENDENT ROBUST CONTROL FOR UNCERTAIN SINGULAR TIME‐DELAY SYSTEMS

ABSTRACTThe problem of delay‐dependent robust stabilization for uncertain singular time‐delay systems is investigated in this paper. The parameter uncertainty is assumed to be norm‐bounded and possibly time‐varying, while the time delay considered here is assumed to be constant but unknown. A delay‐dependent condition is presented for a singular time‐delay system to be regular, impulse free, and stable, based on which robust stability analysis and the robust stabilization problem are studied. An explicit expression for the desired state‐feedback control law is also given. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which involve no decomposition of the system matrices. Some numerical examples are given to show the efficiency of the theoretical conditions.