Delay-dependent Absolute Stability Criteria Research Articles

An improved stability criterion for discrete-time time-delayed Lur'e system with sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur'e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach.

Further results on absolute stability of Lur׳e systems with a time-varying delay

In this paper, we focus on the problem of absolute stability of Lur׳e systems with time-varying delay and sector-bounded nonlinearity. An improved free-matrix-based inequality (FMBI) is derived. By using this inequality and the convex combination technique, some new delay-dependent absolute stability criteria are derived. These conditions are given in the term of linear matrix inequalities (LMIs) and accordingly can be readily solved and checked. Finally, a numerical example is solved using the proposed method to demonstrate the effectiveness and its improvement over existing ones.

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.

On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.

A Delay Decomposition Approach to Robust Absolute Stability of Neutral Lurie Control System

This paper investigates the robust absolute stability problem for the neutral Lurie indirect control systems with time-varying delays. A delay decomposition approach is proposed to deal with the stability problem. With different limitations, some delay-dependent robust absolute stability criteria are presented by choosing proper Lyapunov functions. Finally, some examples are given to illustrate the significances of the criteria.

Delay-dependent absolute stability criterion for Lurie system with probabilistic interval time-varying delay

In this paper, the absolute stability of Lurie control system with probabilistic time-varying delay is studied. By using a new extended Lyapunov-Krasovskii functional, an improved stability criterion based on LMIs is presented and its solvability heavily depends on the sizes of both the delay range and its derivatives, which has wider application fields than those present results. The efficiency and reduced conservatism of the presented results can be demonstrated by two numerical examples with giving some comparing results.

New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.

Absolute Stability Condition for T-S Fuzzy Lurie Control Systems with Time Delay

This paper is concerned with the absolute stability of a new class of Takagi-Sugeno (T-S) fuzzy Lurie control systems with time-delay in the state. By using novel techniques, a new delay-dependent absolute stability criterion described in the form of LMIs. Finally, a numerical example and its simulation results are provided to illustrate feasibility and effectiveness of the proposed result.

A New Delay-dependent Absolute Stability Criterion for Lurie Systems with Time-varying delay

A New Delay-dependent Absolute Stability Criterion for Lurie Systems with Time-varying delay

A New Delay-dependent Absolute Stability Criterion for Lurie Systems with Time-varying delay

The problem of absolute stability analysis for Lurie systems with time-varying delay and norm-bounded parameter uncertainties is considered. By using a new Lyapunov-Krasovskii functional, which splits the whole delay interval into two subintervals and defining a different energy function on each subinterval, some new delay-dependent robust absolute stability criteria are presented in terms of strict linear matrix inequalities (LMIs). The obtained delay-dependent criteria are less conservative than previous ones, which are illustrated by numerical examples.

A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems

This paper deals with absolute stability for a class of nonlinear neutral systems using a discretized Lyapunov functional approach. A delay-dependent absolute stability criterion is obtained and formulated in the form of linear matrix inequalities (LMIs). The criterion is valid not only for systems with small delay, but also for systems with non-small delay. Neither model transformation nor bounding technique for cross terms, nor free weighting matrix method is involved through derivation of the stability criterion. Numerical examples show that for small delay case, the results obtained in this paper significantly improve the estimate of the stability limit over some existing result in the literature; for non-small delay case, the ideal results can also be achieved.

Absolute stability of Lur'e systems with time-varying delay

The problem of the absolute the stability of Lur'e systems with time-varying delay is addressed. Full consideration is given to two cases of time-varying delays – one being continuous-uniformly bounded and the other being differentiable-uniformly bounded with the derivative of the delay bounded by a constant. Some delay-dependent absolute-stability criteria are derived and formulated in the form of linear matrix inequalities. The relationship between the absolute stability criteria for the two cases of time-varying delays is built. A numerical example shows the effectiveness of the obtained results.

Robust stability for delay Lur'e control systems with multiple nonlinearities

This paper deals with delay Lur'e control systems with multiple nonlinearities and time-varying structured uncertainties. First, some sufficient, and necessary and sufficient conditions for the existence of a Lyapunov functional in the extended Lur'e form with a negative definite derivative that guarantees delay-independent robust absolute stability are presented. Then, some new less conservative delay-dependent absolute stability criteria are derived that employ free weighting matrices to express the relationships between the terms in the Leibniz–Newton formula. All the criteria are based on linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the method.