Lurie Control Systems Research Articles

Robust absolute stability of Lurie interval control systems

AbstractThis paper considers robust absolute stability of Lurie control systems. Particular attention is given to the systems with parameters having uncertain, but bounded values. Such so‐called Lurie interval control systems have wide applications in practice. In this paper, a number of sufficient and necessary conditions are derived by using the theories of Hurwitz matrix, M matrix and partial variable absolute stability. Moreover, several algebraic sufficient and necessary conditions are provided for the robust absolute stability of Lurie interval control systems. These algebraic conditions are easy to be verified and convenient to be used in applications. Three mathematical examples and a practical engineering problem are presented to show the applicability of theoretical results. Numerical simulation results are also given to verify the analytical predictions. Copyright © 2007 John Wiley & Sons, Ltd.

Delay-dependent absolute stability of Lurie control systems with multiple time-delays

The stability of Lurie control systems with multiple time-delays is investigated. The system with multiple time-delays is transformed, then a suitable Lyapunov function is selected, the delay-dependent absolutely stable condition for Lurie control systems with multiple time-delays is obtained by applying the technique of analyzing inequality and the method of decomposing the matrices. The condition is based on the linear matrix inequality. Finally, a numerical example is given to demonstrate the derived condition is less conservative than that given in the literature.

Sufficient and necessary conditions for absolute stability of time-delayed Lurie control systems

In this paper, we present some sufficient and necessary conditions for the absolute stability of time-delayed Lurie control systems, which improve the results we obtained before for the absolute stability of direct control, indirect control and critical control of Lurie systems. We also derived certain simple and easy applicable algebraic sufficient conditions for the absolute stability of time-delayed Lurie control systems, which provide a convenient tool for practical control engineers in designing absolutely stable systems or stabilizing nonlinear control systems.

Lyapunov function of general Lurie systems with multiple nonlinearities

In this paper, the absolute stability problem of general Lurie control system with multiple nonlinearities is investigated. Some new necessary and sufficient conditions are obtained for the existence of Lyapunov function of extended Lurie form with negative definite and negative semidefinite derivatives. From these conditions, some very general algebraic criteria for absolute stability are obtained, which extend and generalize previous work on the subject. A numerical example is presented to illustrate the effectiveness of the new criteria.

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

In this paper, the problem of absolute stability for general Lurie control systems with multi-nonlinear feedback terms is investigated. From the Lyapunov function approach, new necessary and sufficient conditions and some practical sufficient conditions of absolute stability are derived, which improve the absolute stability for the set. A numerical example illustrates the effectiveness of the proposed results.

Lyapunov Functional for Multiple Delay General Lurie Systems with Multiple Non-linearities

In this paper, the absolute stability problem of a multiple delay general Lurie control system with multiple non-linearities is considered. Necessary and sufficient conditions are obtained for the existence of the Lyapunov functional of extended Lurie form with negative definite derivative. From those conditions, a very general algebraic criterion for absolute stability is obtained, which extends the previous results. A concise example illustrates the effectiveness of the present results.

Necessary and sufficient conditions for the absolute stability of discrete type lurie control system

In this paper, it is discussed that the obsolute stability for zero solution of the discrete type Lurie control system (1) $$\left. {\begin{array}{*{20}c} {x(n + 1) = Ax(n) + bf[\sigma (n)]} \\ {\sigma (n) = c^T x(n)} \\ \end{array} } \right\}$$ in which the nonlinear function f(δ) satisfying conditions as follows (2) $$\begin{array}{*{20}c} {f(0) = 0,\sigma f(\sigma ) > 0} & {(\sigma \ne 0)} \\ \end{array}$$ or (3) $$\begin{array}{*{20}c} {f(0) = 0,0 \leqslant k_1 \leqslant f(\sigma )/\sigma \leqslant k_2< + \infty } & {(\sigma \ne 0)} \\ \end{array}$$ It gives the necessary and sufficient conditions for the absolute stability for system (1) under conditions (2). We also obtain the sufficient criteria for absolute stability of the simplified system of (1) under conditions (3).

ABSOLUTE STABILITY OF GENERAL LURIE CONTROL SYSTEMS

In this paper, we investigate the absolute [stability of the general Lurie control systems. The necessary and sufficient conditions for absolute stability are obtained. These conditions can be readily checked and are convenient in application.