Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances

The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ϵ-convergent, which means that the estimate converges robustly within an ϵ-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ϵ-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ϵ. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.

Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.

Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

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.

Partial-state observers for nonlinear systems

This note deals with the design of reduced-order observers for a class of nonlinear systems. The order reduction of the observer is achieved by only estimating a required partial set of the state vector. Necessary and sufficient conditions are derived for the existence of reduced-order observers. An observer design procedure based on linear matrix inequalities is given. A numerical example is given to illustrate the design method.

Exponential stabilization of neural networks with various activation functions and mixed time-varying delays

This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.

Parameter-dependent H∞ control for time varying delay polytopic systems

This paper addresses the robust stabilization and H_∞ control problem for a class of linear polytopic systems with continuously distributed delays. The control objective is to design a robust H_∞ controller that satisfies some exponential stability constraints on the closed-loop poles. Using improved parameter-dependent Lyapunov Krasovskii functionals, new delay-dependent conditions for the robust H_∞ control are established in terms of linear matrix inequalities.

Efficient subwindow search with submodular score functions

Subwindow search aims to find the optimal subimage which maximizes the score function of an object to be detected. After the development of the branch and bound (B&B) method called Efficient Subwindow Search (ESS), several algorithms (IESS [2], AESS [2], ARCS [3]) have been proposed to improve the performance of ESS. For nn images, IESS's time complexity is bounded by O(n³) which is better than ESS, but only applicable to linear score functions. Other work shows that Monge properties can hold in subwindow search and can be used to speed up the search to O(n³), but only applies to certain types of score functions. In this paper we explore the connection between submodular functions and the Monge property, and prove that sub-modular score functions can be used to achieve O(n³) time complexity for object detection. The time complexity can be further improved to be sub-cubic by applying B&B methods on row interval only, when the score function has a multivariate submodular bound function. Conditions for sub-modularity of common non-linear score functions and multivariate submodularity of their bound functions are also provided, and experiments are provided to compare the proposed approach against ESS and ARCS for object detection with some nonlinear score functions.

Observer-based controller design of time-delay systems with an interval time-varying delay

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov–Krasovskii functionals and utilizing the Newton–Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

Design of H∞ control of neural networks with time-varying delays

This paper deals with the H∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov-Krasovskii functionals, we establish new sufficient conditions for H∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

Observer-based control for time-varying delay neural networks with nonlinear observation

This paper studies the problem of designing observer-based controllers for a class of delayed neural networks with nonlinear observation. The system under consideration is subject to nonlinear observation and an interval time-varying delay. The nonlinear observation output is any nonlinear Lipschitzian function and the time-varying delay is not required to be differentiable nor its lower bound be zero. By constructing a set of appropriate Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, some delay-dependent stabilizability conditions which are expressed in terms of Linear Matrix Inequalities (LMIs) are derived. The derived conditions allow simultaneous computation of two bounds that characterize the exponential stability rate of the closed-loop system. The unknown observer gain and the state feedback observer-based controller are directly obtained upon the feasibility of the derived LMIs stabilizability conditions. A simulation example is presented to verify the effectiveness of the proposed result.

H∞ observer-based control for discrete-time one-sided Lipschitz systems with unknown inputs

This paper investigates the problem of robust observer-based stabilization for a class of one-sided nonlinear discrete-time systems subjected to unknown inputs. We propose a simple simultaneous state and input estimator. A nonlinear controller is then proposed to compensate for the effects of unknown inputs and to ensure asymptotic stability in a closed loop. Several mathematical artifacts are used to deduce stability conditions expressed in terms of linear matrix inequalities. To show high performances of the proposed technique, a relevant example is provided with comparisons to recent results.