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.

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.

Exponential stabilization for state and input delay systems via output feedback

This paper considers the exponential stabilization problem via static and dynamic output feedback controllers of linear systems with a time delay in both the state and input. By using a change of the state variable and combining with the Lyapunov-Krasovskii method, new sufficient conditions for exponential stabilization via static and dynamic output feedback controllers are proposed. The conditions are expressed in terms of matrix inequalities but with only one parameter needs to be tuned and therefore can be efficiently solved by incorporating an one-dimensional search method into the Matlab’s LMI toolbox. Two numerical examples are provided to illustrate the obtained results.

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.

Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

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.

Full-order observer design for nonlinear complex large-scale systems with unknown time-varying delayed interactions

This article is concerned with the problem of state observer for complex large-scale systems with unknown time-varying delayed interactions. The class of large-scale interconnected systems under consideration is subjected to interval time-varying delays and nonlinear perturbations. By introducing a set of argumented Lyapunov–Krasovskii functionals and using a new bounding estimation technique, novel delay-dependent conditions for existence of state observers with guaranteed exponential stability are derived in terms of linear matrix inequalities (LMIs). In our design approach, the set of full-order Luenberger-type state observers are systematically derived via the use of an efficient LMI-based algorithm. Numerical examples are given to illustrate the effectiveness of the result