Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Delay-dependent exponential stability of neutral stochastic delay systems (vol 54, pg 147, 2009)

In the above titled paper originally published in vol. 54, no. 1, pp. 147-152) of IEEE Transactions on Automatic Control, there were some typographical errors in inequalities. Corrections are presented here

Integral partitioning approach to stability analysis and stabilization of distributed time delay systems

In this paper, the problems of delay-dependent stability analysis and stabilization are investigated for linear continuous-time systems with distributed delay. By introducing an integral partitioning technique, a new form of Lyapunov-Krasovskii functional (LKF) is constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities (LMIs). Based on the criteria, a design algorithm for a state feedback controller is proposed. The results developed in this paper are less conservative than existing ones in the literature, which is illustrated by several examples. © 2011 IFAC.postprintThe 18th World Congress of the International Federation of Automatic Control (IFAC 2011), Milano, Italy, 28 August-2 September 2011. In Proceedings of the 18th IFAC World Congress, 2011, v. 18 pt. 1, p. 5094–509

Exponential Stabilization of Delay Neutral Systems under Sampled-Data Control

International audienceThis paper considers the exponential stabilization of delay systems of the neutral type via sampled-data control. The control input of the neutral system can present a delay, constant or variable. The sampling period is not necessarily constant. It is only assumed that the time between to successive sampling instants is bounded. Since the sampling effect (sampling and zero-holder) is equivalent to a variable delay, the resulting system is modelled as a continuous-time one, where the control input has a ‘non-small' time-varying delay belonging to some interval [h−μ,h+μ]. For instance, h−μ may represent the minimum input delay, and 2μ the additional delay generated by the combination of the sampling effect with the input delay variation. This results in a system with ‘nonsmall' time-varying delays (i.e. delays with a known and nonzero minimum value), the exponential stabilization of which is possible under LMI conditions. Two examples are provided. The first one deals with the sampled-data control of a neutral system. The second one considers the stabilization of a flexible rod with continuous, delayed control

New positive realness conditions for uncertain discrete descriptor systems: Analysis and synthesis

This paper deals with the problems of positive real (PR) analysis and PR control for uncertain discrete-time descriptor systems. The parameter uncertainties are assumed to be time-invariant norm bounded and appear in both the state and input matrices. A new necessary and sufficient condition for a discrete-time descriptor system to be regular, causal, stable and extended strictly PR (ESPR) is proposed in terms of a strict linear matrix inequality. Based on this, the concepts of strong robust admissibility with ESPR and strong robust admissibilizability with ESPR were introduced. Without any additional assumptions on the system matrices, necessary and sufficient conditions for strong robust admissibility with ESPR and strong robust admissibilizability with ESPR are obtained. Through these results, the problems of PR analysis and PR control are solved. Furthermore, an explicit expression of a desired state feedback controller is also given, which involves no decomposition of the system matrices. © 2004 IEEE.published_or_final_versio

Robust stability and stabilization for singular systems with state delay and parameter uncertainty

This note considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.published_or_final_versio

Stabilization of Neutral Systems with Saturating Control Inputs

International audienceThis paper focuses on the stabilization problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimization problems with LMI constraints are therefore proposed to compute stabilizing state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results

Robust Stabilization of Neutral Systems with Saturating Inputs

International audienceThis paper focuses on the stabilization problem of neutral systems in the presence of control saturation. Based on a descriptor approach and the use of a modified sector condition, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions allow to consider systems presenting time-varying delays and are formulated directly as linear matrix inequalities (LMIs). Optimization problems are formulated with the aim of computing stabilizing state feedback control laws

Robust sampled-data control: An input delay approach

International audienceA method for robust sampled-data stabilization of linear continuous-time systems is introduced. This method is based on the continuous-time model with time-varying input delay. Delay-dependent sufficient LMIs conditions for stabilization of systems with polytopic type uncertainty and for regional stabilization of systems with sampled-data saturated state-feedback are derived. The method may be applied to a wide spectrum of robust sampled-data control problems