Observer design for lipschitz nonlinear systems with time-varying output and state delays

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

This paper establishes a framework for stability analysis and memoryless state-feedback control synthesis of linear discrete-time systems with time varying state delay. The underlying idea is converting the considered system into an equivalent constrained switched system, leading to sufficient and necessary condition for stability analysis. Based on this switched system modeling, available information about the time-varying delay such as known bounds of variation rate can be incorporated into the analysis in a natural way. Moreover, sufficient conditions for memoryless state-feedback control design are obtained in a similar style. The analysis and synthesis conditions are given in terms of solvability of a set of linear matrix inequalities (LMIs). Numerical examples are included for illustration.

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.

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.

Delayed finite-dimensional observer-based control of 1-D parabolic PDEs

This paper investigates the stabilization problem for Takagi-Sugeno fuzzy systems subjected to both fixed state delays and unknown time-varying output delays. First, a novel fuzzy observer is proposed to synchronously estimate the system state and the disturbance term caused by the unknown output delays. Then, along with the fuzzy observer, a fuzzy controller is designed to ensure the stability of the overall system by Lyapunov-based analysis. Finally, the effectiveness and correctness of the obtained results are verified by simulation example.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

Decentralized piecewise [formula omitted] fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay

A robust controller is developed for uncertain, second-order nonlinear\nsystems subject to simultaneous unknown, time-varying state delays and known,\ntime-varying input delays in addition to additive, sufficiently smooth\ndisturbances. An integral term composed of previous control values facilitates\na delay-free open-loop error system and the development of the feedback control\nstructure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals\nguarantees uniformly ultimately bounded tracking under the assumption that the\ndelays are bounded and slowly varying.\n

The robust H∞ control problem for time-varying uncertain linear systems with time-varying state, and control delays is considered. Based on the Riccati equation approach, we design a robust H∞ linear time-invariant state feedback control law, which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A sufficient condition for the existence of the. robust H∞ controller is derived and two synthesis methods are presented for a robust H∞ control law to uncertain time-delay systems. One is to construct a robust H∞ control law by an equivalent linear time-invariant structural description for the sufficient condition and the control law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMF) problem and the control law can be obtained by solving the LMI. A numerical example is presented to illustrate the obtained results.

Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

The dissipative analysis and control synthesis for uncertain singular systems with interval time-varying state and input delays are investigated in this paper. The parametric uncertainty in this paper is assumed to be norm bounded. A sufficient condition, in the form of linear matrix inequality (LMI) with nonlinear constraints, on the existence of robust dissipative controller is established based on the Lyapunov stability theory. In order to solve the nonlinear problem, Cone Complementarity Linearization (CCL) is offered.

This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Moreover, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness and improvement over some existing results in the literature.

This paper presents a state observer for linear systems and Lipschitz nonlinear systems with delayed output measurements, which are affected by a known and bounded time-varying delay. The structure of the proposed observer is based on a proportional-integral term, which allows to compensate the time-varying delay. The observer gain depends on the maximum bounded delay. This gain is computed by a Linear Matrix Inequality (LMI) approach. The observer exhibits good performance for state estimation of the system despite the presence of significantly long delay. A Lyapunov-Krasovskii functional is used to prove the asymptotical convergence to zero of the observation error. This observer is applied to the case of systems with time-varying delay whose dynamic is described by a piecewise differentiable function. Examples and numerical simulations are provided in order to support the validity of the main results.

Autonomous systems often use feedback from an imaging system for guidance, navigation, and control. Such feedback requires an image processing method that yields an inherent delay in state measurements. For some camera-to-hand applications, the image-based sensing and control computations may be computed by a more capable processor and then be transmitted to a sensorless vehicle, resulting in a delay in control execution. To account for these delays, an approach is developed in this paper that applies a transformation, to separate the image coordinates into spatial and time domain components. This transformation, along with a novel integral error system, allows for the development of a robust controller that compensates for uncertain time-varying state delays and known time-varying input delays for nonlinear image dynamics. A Lyapunov-based stability analysis is used to prove that the developed controller enables a sensorless autonomous vehicle to yield uniformly ultimately bounded (UUB) tracking of a desired image trajectory.