Delay-dependent Stability For Linear Systems Research Articles

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This paper considers the delay-dependent stability of linear systems with a time-varying delay in the frame of the Lyapunov-Krasovskii functional(LKF) approach. First, we choose an LKF that is the form of a constrained quadratic function(CQF) for the delay in its time-derivative and a quadratic integral. Second, the Bessel-Legendre inequality and the reciprocally convex inequality are used to find the upper bound of the quadratic integral. Third, a new form of necessary and sufficient condition is adopted to equivalently transform the CQF into the form of Linear matrix inequality(LMI). Finally, two well-known numerical examples are given to show the usefulness of the proposed result.

New Lyapunov-Krasovskii Functional for Stability Analysis of Linear Systems with Time-Varying Delay

This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delay. A new delay-product-type augmented Lyapunov-Krasovskii functional (LKF) is constructed. Based on the LKF and by employing a generalized free-matrix-based integral inequality, less conservative delay-dependent stability criteria are obtained. Finally, two well-known numerical examples are used to confirm the effectiveness and the superiority of the presented stability criteria.

New Criterion for Stability of Linear Systems with Interval Time-Varying Delay

This paper is concerned with the delay-dependent stability for linear systems. Through constructing a new augmented LKF and using a new integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities, and it is established that the results have less conservativ`e than some existing stability conditions. Finally, numerical examples are given to illustrate the effectiveness of the proposed result.

Delay-dependent stability criteria for linear systems with multiple time delays

The problem of the delay-dependent stability of linear systems with multiple time delays is discussed. A new method is first presented for a system with two time delays, in which free weighting matrices are used to express the relationships among the terms of the Leibniz-Newton formula. Next, this method is used to show the equivalence between a system with two identical time delays and a system with a single time delay. Then, a numerical example verifies that the criterion given is effective and is a significant improvement over the existing ones. Finally, the basic idea is extended to a system with multiple time delays.

New results for delay-dependent stability of linear systems with time-varying delay

The asymptotic stability problem for a class of linear systems with time-varying delays is studied using a generalized discretized Lyapunov functional approach. The kernel of the functional, which is a function of two variables, is chosen as piecewise linear. The conditions of the Lyapunov functional and its derivative are written in terms of linear matrix inequalities (LMIs). New delay-dependent stability criteria are proposed by simplifying the derived LMIs. Numerical examples show that the results obtained by these new criteria significantly improve the estimate of stability limit over the existing results in the literature.

Mixed Delay-Independent / Delay-Dependent Stability of Linear Systems With Delayed State: An L.M.I. Approach

This paper focuses on some delay-independent / delay-dependent asymptotic stability problems of a class of linear systems described by delay-differential equations involving several constant (or time-varying) delays. We give sufficient conditions (expressed in terms of LMIs) for characterizing unbounded stability regions in the delays parameter space. Note that the presented results allow to recover previous sufficient delay-independent or delay-dependent conditions from the control literature.