Stability Condition For Uncertain Systems Research Articles

Novel robust stability condition for uncertain systems with interval time-varying delay and nonlinear perturbations

Novel robust stability condition for uncertain systems with interval time-varying delay and nonlinear perturbations

Novel robust stability condition for uncertain systems with interval time-varying delay and nonlinear perturbations

In this paper, the problem of robust stability analysis for a class of uncertain systems with interval time-varying delay and nonlinear perturbations is studied. In order to develop a less conservative stability condition, a Lyapunov-Krasovskii functional (LKF) comprising quadruple-integral term is introduced. A novel delay dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by using a new delay-partitioning approach and reciprocally convex combination technique, which is derived by integral inequality approach (IIA). Compared with the existing literature, this criterion can greatly reduce the complexity of theoretical derivation and computation. Finally, three well-known numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion.

양자화와 오버플로우 비선형성을 가지는 이산시간 폴리토픽 불확실 지연 시스템의 강인 안정성

In this paper, we consider the delay-dependent robust stability condition for polytopic uncertain systems with interval time-varying delay using various combinations of quantization and overflow nonlinearities. A robust stability condition for uncertain systems with time-varying delay and quantization/overflow nonlinearities is proposed by LMI(linear matrix inequality) and Lyapunov technique. It is shown that the proposed method is less conservative compared to the recent results by numerical examples.

Sharp Bounds for Lyapunov Exponents and Stability Conditions for Uncertain Systems With Delays

Stability of a set of systems with norm bounded nonlinear terms and arbitrary time-varying as well as distributed delays is studied. A novel approach to this problem, based on deriving bounds for the norms of system solutions, is developed. A sharp estimate for the maximal Lyapunov exponent of the solutions, expressed in the bounds for the uncertain parameters, is found. The subsystems, for which the obtained estimate is attained, are indicated. Using these results, a delay-independent necessary and sufficient stability condition for the considered set of systems is derived. For a system with prescribed parameters, sufficient conditions for exponential stability and upper bound for the maximal Lyapunov exponent are obtained. The proposed approach is applied to illustrative examples which contrast its efficiency.

Eigenstructure assignment-based robust stability conditions for uncertain systems with multiple time-varying delays

The problem of robust stability of dynamical systems with multiple time-varying delays and structured state-space uncertainties is discussed. Based on the fact that the dynamic response of a multivariable control system can be modified by means of eigenstructure assignment, a method is presented whereby a new sufficient condition for robust stability of such uncertain time-delay systems is derived. The new robust stability condition is a sum of terms, each of which involves the ith right eigenvector, the ith left eigenvector, and the real part of the ith eigenvalue, and is shown to be less conservative than the earlier result reported in the control literature. Here, each time-varying delay is assumed only to be any bounded, continuous non-negative function, and the derived robust stability condition is independent of the delay. Therefore our results are also applicable to systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.