Delay-dependent robust stability analysis for systems with interval delays

This paper is concerned with the stability analysis for uncertain systems with interval time-varying delays. An appropriate class of Lyapunov-Krasovskii functionals is proposed and, splitting the known bounds of the delay interval in two subintervals, a new delay-dependent criterion is derived. In addition, we resort to the use of a polytope to introduce a novel treatment of the time-varying delays. A number of different examples are given to demonstrate the reduced conservatism of this method

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method

Robust Control of Uncertain Time -Delay Systems.

Time-delay systems are common in industries. Direct analysis and synthesis of control systems with time delays are complicated and approximation methods such as Pade approximation are usually applied. However, the issues of control system robustness with respect to model uncertainties and approximation errors have not been sufficiently addressed. This dissertation focus on robustness of time-delay systems, especially robustness with respect to time delays, which has been discussed extensively using Lyapunov second method. We propose two methods in this dissertation to reformulate the problems into standard mu or Hinfinity problems. The first method involves representing the systems in linear functional transformation (LFT) framework and approximating delays by rational transfer functions. The approximation errors are then treated as uncertainties. We show that all the well-known techniques of Hinfinity control theory can be applied to this framework. Consequently, controller design becomes a routine process. We also show that the conventional Lyapunov method is a special case in our proposed framework and our proposed method offers less conservative results. In the second method, we treat uncertain delays as uncertainties with restricted phase angles and extend structured singular value to include phase information. We show that the extended small-mu theorem can be applied to analyze stability and performance of uncertain delay systems with many other type of uncertainties, such as plant model uncertainties and parametric uncertainties. Finally, we generalize the above techniques to linear systems with feedback connected nonlinear elements. Both time invariant and time-varying nonlinearities are discussed by incorporating circle/Popov criterion with small-mu theorem

Analysis and Design of Singular Markovian Jump Systems

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H? control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H? control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H? filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course

Stability of networked control systems with large delays

Abstract — We consider the stabilization problem for Net-worked Control Systems (NCSs) with uncertain, time-varying network-induced delays and a bounded number of subsequent packet dropouts. A discrete-time model, describing a NCS with packet dropouts and time-varying delays, that can be both smaller and larger than the sampling interval, is presented. Based on this NCS model sufficient LMI conditions are pro-posed for the stability analysis and controller synthesis problem for two different controllers, i.e. a feedback controller that depends on both the state and the past control inputs and a state-feedback controller. The applicability of both controllers is compared. Moreover, the stability and controller synthesis LMIs allow for a performance analysis in terms of a lower bound for the transient decay rate of the response. The results are illustrated by application to a typical motion control example. I

Time-delay systems : stability, sliding mode control and state estimation

University of Technology, Sydney. Faculty of Engineering and Information Technology.Time delays and external disturbances are unavoidable in many practical control systems such as robotic manipulators, aircraft, manufacturing and process control systems and it is often a source of instability or oscillation. This thesis is concerned with the stability, sliding mode control and state estimation problems of time-delay systems. Throughout the thesis, the Lyapunov-Krasovskii (L-K) method, in conjunction with the Linear Matrix Inequality (LMI) techniques is mainly used for analysis and design. Firstly, a brief survey on recent developments of the L-K method for stability analysis, discrete-time sliding mode control design and linear functional observer design of time-delay systems, is presented. Then, the problem of exponential stability is addressed for a class of linear discrete-time systems with interval time-varying delay. Some improved delay-dependent stability conditions of linear discrete-time systems with interval time-varying delay are derived in terms of linear matrix inequalities. Secondly, the problem of reachable set bounding, essential information for the control design, is tackled for linear systems with time-varying delay and bounded disturbances. Indeed, minimisation of the reachable set bound can generally result in a controller with a larger gain to achieve better performance for the uncertain dynamical system under control. Based on the L-K method, combined with the delay decomposition approach, sufficient conditions for the existence of ellipsoid-based bounds of reachable sets of a class of linear systems with interval time-varying delay and bounded disturbances, are derived in terms of matrix inequalities. To obtain a smaller bound, a new idea is proposed to minimise the projection distances of the ellipsoids on axes, with respect to various convergence rates, instead of minimising its radius with a single exponential rate. Therefore, the smallest possible bound can be obtained from the intersection of these ellipsoids. This study also addresses the problem of robust sliding mode control for a class of linear discrete-time systems with time-varying delay and unmatched external disturbances. By using the L-K method, in combination with the delay decomposition technique and the reciprocally convex approach, new LMI-based conditions for the existence of a stable sliding surface are derived. These conditions can deal with the effects of time-varying delay and unmatched external disturbances while guaranteeing that all the state trajectories of the reduced-order system are exponentially convergent to a ball with a minimised radius. Robust discrete-time quasi-sliding mode control scheme is then proposed to drive the state trajectories of the closed-loop system towards the prescribed sliding surface in a finite time and maintain it there after subsequent time. Finally, the state estimation problem is studied for the challenging case when both the system’s output and input are subject to time delays. By using the information of the multiple delayed output and delayed input, a new minimal order observer is first proposed to estimate a linear state functional of the system. The existence conditions for such an observer are given to guarantee that the estimated state converges exponentially within an Є-bound of the original state. Based on the L-K method, sufficient conditions for Є-convergence of the observer error, are derived in terms of matrix inequalities. Design algorithms are introduced to illustrate the merit of the proposed approach. From theoretical as well as practical perspectives, the obtained results in this thesis are beneficial to a broad range of applications in robotic manipulators, airport navigation, manufacturing, process control and in networked systems

Robustness analysis of discrete predictor-based controllers for input-delay systems

In this article, robustness to model uncertainties are analysed in the context of discrete predictor-based state-feedback controllers for discrete-time input-delay systems with time-varying delay, in an LMI framework. The goal is comparing robustness of predictor-based strategies with respect to other (sub)optimal state feedback ones. A numerical example illustrates that improvements in tolerance to modelling errors can be achieved by using the predictor framework.The authors are grateful for grant nos. DPI2008-06737-C02-01, DPI2008-06731-C02-01, DPI2011-27845-C02-01 and PROMETEO/2008/088 from the Spanish and Valencian governments.González Sorribes, A.; Sala, A.; García Gil, PJ.; Albertos Pérez, P. (2013). Robustness analysis of discrete predictor-based controllers for input-delay systems. International Journal of Systems Science. 44(2):232-239. https://doi.org/10.1080/00207721.2011.600469S232239442Boukas, E.-K. (2006). 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