Stability of Systems with Distributed Delays (original) (raw)

Robust stability conditions for systems with distributed delays

Robust stability conditions for systems with distributed delays are presented. The result is derived within the approach of Lyapunov-Krasovskii functional of complete type. Here, the prescribed derivative includes general cross terms. As a consequence the robustness margins are less conservative than those obtained in previous contributions

Graphical test for robust stability with distributed delayed feedback

Lecture Notes in Control and Information Sciences, 1998

The performance of a nominally designed state feedback control for a linear systems is analyzed in the case that the information, available at time t for feedback, consists of a functional of the state over the interval It-T, t]. Sufficient conditions are given for the stability and asymptotic stability, independent of the matrix valued weight functions on the delay-perturbed state. These sufficient conditions, obtained via the Lyapunov-Krasovskii theory, revolve around the existence of some positive definite matrix functions satisfying certain Riccati-type differential equations. Connections are made with the theory of robust control and its frequency domain criteria. New graphical criteria akin to the Nyquist criterion are derived to obtain the delay perturbation margin.

Stabilization of distributed control systems with delay

Systems & Control Letters, 2011

In this paper the asymptotic stabilization of linear distributed parameter control systems with delay is considered. Specifically, we are concerned with the class of control systems described by the equation

Robust Stabilization of Linear Systems with Delayed State and Control

Journal of Optimization Theory and Applications, 2008

Robust stabilization of linear systems with delays on both the state and control input is studied in this paper. Using an improved Lyapunov-Krasovskii functional, we establish new criteria that ensure the robust stability of the closed-loop system with memoryless state feedback controls. The generalized conditions are derived in terms of linear matrix inequalities (LMIs), allowing us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution and can be easily solved by numerical algorithms. Keywords Stabilization • Robust control • Delayed state and control • Uncertainties • Lyapunov functional • Linear matrix inequality Communicated by F.E. Udwadia. This work was supported by the National Basic Program in Natural Sciences. The authors thank the anonymous referees for valuable comments to improve the paper.

An improved stability criterion for systems with distributed delays

International Journal of Robust and Nonlinear Control, 2003

This article improves the formulation of discretized Lyapunov functional method for systems with distributed delays. The main idea is to apply Jensen's inequality and variable elimination in matrix inequalities. The resulting stability criterion is much simpler. Experience in numerical calculation indicates that it generally converges to the analytical result as grid size decreases, and the speed of convergence is much faster than the previous method. The new formulation is also applicable to a wider class of systems.

LMI based control design for linear systems with distributed time delays

Archives of Control Sciences, 2012

The paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.

Robust and H∞ stabilisation of interconnected systems with delays

IEE Proceedings - Control Theory and Applications, 1998

The problems of decentralised robust stabilisation and robust H , performance for a class of interconnected systems with unknown delays and norm-bounded parametric uncertainties are addressed in the paper. The delays are time-varying in the state of each subsystem as well as in the interconnections among the subsystems. A class of decentralised observer-based feedback controllers is developed to render the closed-loop interconnected system asymptotically stable. All the design effort is undertaken at the subsystem level. It is shown that the robust control design problems can be solved with the aid of two algebraic Riccati inequalities. The developed theory is illustrated by simulation of a multireach pollution model of a representative segment of the River Nile.

New delay-dependent stability conditions for linear system with delay

2011

In this work, delay-dependent stability conditions for systems described by delayed differential equations are presented. The employment of a special transformation to a state space representation named Benrejeb characteristic arrow matrix permits to determine new asymptotic stability conditions. Illustrative examples are presented to show the effectiveness of the proposed approach.

Stabilization of linear distributed control systems with unbounded delay

Journal of Mathematical Analysis and Applications, 2005

In this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay. Assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space, we characterize those systems that can be stabilized using a feedback control. As consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control.

New delay-dependent stability conditions for linear systems with delay

In this work, delay-dependent stability conditions for systems described by delayed differential equations are presented. The employment of a special transformation to another state space representation named Benrejeb characteristic arrow matrix permit to determine a practical asymptotic stability condition. An Illustrative example is presented permitting to understand the application of the proposed methods.