Relative controllability of nonlinear neutral systems with multiple delays in state and control

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper we study the relative controllability of nonlinear neutral system with distributed and multiple lumped time varying delays in control. Using Schauder's fixed point theorem sufficient conditions for relative controllability in a given time interval are formulated and proved. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 565-570

The problem of robust H/spl infin/ filtering for continuous-time uncertain linear systems with multiple time-varying delays in the state variables is investigated. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The aim is to design a stable linear filter assuring asymptotic stability and a prescribed H/spl infin/ performance level for the filtering error system, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities, which can be efficiently solved by means of powerful convex programming tools with global convergence assured. An example illustrates the proposed methodology.

This chapter introduces the Internally Positive Representation of linear systems with multiple time-varying state delays. The technique, previously introduced for the undelayed case, aims at building a positive representation of systems whose dynamics is, in general, indefinite in sign. As a consequence, stability criteria for positive time-delay systems can be exploited to analyze the stability of the original system. As a result, an easy-to-check sufficient condition for the delay-independent stability is provided, that is compared with some well known conditions available in the literature.

In this note, the problem of delay-dependent robust stabilization for singular systems with multiple time-varying state delays has been investigated, and the problem is solved via state feedback controller in terms of a linear matrix inequality technique. Numerical examples are given to show the validity of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

The robust passivity synthesis problem is addressed for a class of uncertain delayed systems with time-varying delays in both state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all the matrices of the model. The problem aims at designing an observer-based dynamic controller that renders the closed-loop systems strongly robustly stable with strictly passive for all admissible uncertainties, dependently of the maximum of delay derivative. By converting the problem at present into a class of strongly stable with strictly passive control problem for some parameterized systems equivalently, the explicit solution is established and expressed in terms of a linear matrix inequality.

An output feedback model reference adaptive controller is developed for a class of linear systems with multiple unknown time-varying state delays and in the presence of actuator failures. The adaptive controller is designed based on SPR-Lyapunov approach and is robust with respect to multiple unknown time-varying plant delays and to an external disturbance with unknown bounds. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov-Krasovskii functional and Simulation results are provided to demonstrate the effectiveness of the proposed controller.

In this paper, the controllability of nonlinear impulsive fractional dynamical system with delays in state and control is analyzed by using a delayed Mittag Leffler (M-L) function. Controllability Grammian matrix is used to establish the controllability of linear system. The sufficient conditions of the considered nonlinear system are derived by utilizing the fixed point techniques. Finally, an example is provided for the illustration of the obtained result.

In this paper, we are concerned with the controllability of damped second-order integrodifferential systems with impulses. Further the result is extended to study the controllability of nonlinear neutral systems with nonlocal conditions. The fixed point analysis approach is adopted in investigation. Sufficient conditions are formulated with a noncompact condition on the cosine family of operators. The results are obtained using the Banach fixed point theorem. An example is presented to illustrate the results.

The problem of robust H/sub /spl infin// filtering for discrete-time uncertain linear systems with multiple state delays is addressed. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Sufficient conditions for the existence of a stable linear filter assuring stability and a prescribed H/sub /spl infin// performance for the filtering error system for all allowed uncertainties are established in terms of linear matrix inequalities. Efficient numerical algorithms can be used to solve the problem, as illustrated via an example.

In this work, the tracking control problem of nonlinear system which contains unknown parameters, multiple state delays, external disturbances and the dead-zone input is studied. By introducing a dynamic gain-based adaptive control strategy and employing a new Lyapunov–Krasovskii (L–K) functional, we construct an adaptive tracking controller to ensure the boundedness of all the states and guarantee the tracking error small enough. Two examples are given to verify the correctness of the control theory.

In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α,β ≤ 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory.

Sufficient conditions for global relative controllability of certain types of nonlinear time-varying systems with time-variable delay in control are given. The results are obtained by using Schauder's fixed-point theorem. The results obtained are a generalization of Davison [3].

Sufficient conditions for global relative controllability of nonlinear systems with time-varying multiple delays in control and implicit derivatives are derived. The special case, when the delays are constant, is also considered and an example is provided. The results are obtained using the measure of noncompactness of a set and Darbo's fixed-point principle.

H∞ filtering for networked systems with partly known distribution transmission delays