A test for stability robustness of linear time‐varying systems utilizing the linear time‐invariant ν‐gap metric

A stability robustness test is developed for internally stable, nominal, linear time‐invariant (LTI) feedback systems subject to structured, linear time‐varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ν‐gap metric framework. The scaled LTI ν‐gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ν‐gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd.     

Global stability results for systems under sampled‐data control

In this work sufficient conditions for uniform input‐to‐output stability and uniform input‐to‐state stability are presented for finite‐dimensional systems under feedback control with zero‐order hold. The conditions are expressed by means of single and vector Lyapunov functions. Copyright © 2008 John Wiley & Sons, Ltd.     

Delay‐dependent robust stability and stabilization for uncertain discrete singular systems with delays

The robust stability and robust stabilization for time‐delay discrete singular systems with parameter uncertainties is discussed. A delay‐dependent linear matrix inequality (LMI) condition for the time‐delay discrete systems to be nonsingular and stable is given. Based on this condition and the restricted system equivalent transformation, the delay‐dependent LMI condition is proposed for the time‐delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilization are solved, and the delay‐dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the method given in the paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new adaptive backstepping Coulomb friction compensator for servo control systems

A new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time‐derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time‐variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability of nonlinear hybrid dynamical systems with time delay via sum of squares decomposition

Considering an infinite number of eigenvalues for time delay systems, it is difficult to determine their stability. We have developed a new approach for the stability test of time delay nonlinear hybrid systems. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are found, stability’s analysis of the system is straight-forward. In this paper both delay-independent and delay-dependent stability tests are proposed, based on the construction of appropriate Lyapunov-Krasovskii functionals. The methodology is based on the sum of squares decomposition of multivariate polynomials and the algorithmic construction is achieved through the use of semidefinite programming. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be computationally infeasible to solve. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Finally simulation results show the correctness and validity of the designed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. The authors wish to express their thanks to Dr. A. Papachristodoulou and Dr. M. Peet for their helpful comments and suggestions. Mohammad Ali Badamchizadeh was born in Tabriz, Iran, in December 1975. He received the B.S. degree in Electrical Engineering from University of Tabriz in 1998 and the M.Sc. degree in Control Engineering from University of Tabriz in 2001. He received the Ph.D. degree in Control Engineering from University of Tabriz in 2007. He is now an Assistant Professor in the Faculty of Electrical and Computer Engineering at University of Tabriz. His research interests include Hybrid dynamical systems, Stability of systems, Time delay systems, Robot path planning. Sohrab Khanmohammadi received the B.S. degree in Industrial Engineering from Sharif University, Iran in 1977 and the M.Sc. degree in Automatic from University Paul Sabatie, France in 1980 and the Ph.D. degree in Automatic from National University, ENSAE, France in 1983. He is now a Professor of Electrical Engineering at University of Tabriz. His research interests are Fuzzy control, Artificial Intelligence applications in control and simulation on industrial systems and human behavior. Gasem Alizadeh was born in Tabriz, Iran in 1967. He received the B.S. degree in Electrical Engineering from Sharif University, Iran in 1990 and the M.Sc. degree from Khajeh Nasir Toosi University, Iran in 1993 and the Ph.D. degree in Electrical Engineering from Tarbiat Modarres University, Iran in 1998. From 1998, he is a Member of University of Tabriz in Iran. His research interests are robust and optimal control, guidance, navigation and adaptive control. Ali Aghagolzadeh was born in Babol, Iran. He received the B.S. degree in Electrical Engineering in 1985 from University of Tabriz, Tabriz, Iran, and the M.Sc. degree in Electrical Engineering in 1988 from the Illinois Institute of Technology, Chicago, IL. He also attended the School of Electrical Engineering at Purdue University in August 1998 where he was also employed as a part-time research assistant and received the Ph.D. degree in 1991. He is currently an Associate Professor of Electrical Engineering at University of Tabriz, Tabriz, Iran. His research interests include digital signal and image processing, image coding and communication, computer vision, and image analysis.     

A Y-channel design for improving zeta potential and surface conductivity measurements using the current monitoring method

This study presents a new Y-channel design for measuring the zeta potential and surface conductance of a solid-liquid pairing using the current monitoring technique. The new design improves the throughput and reliability of the testing apparatus since the displacement between two solutions can be repeated many times without interfering with the experiments. It also increases the accuracy of the measurement by producing sharper start and end transitions for the current–time plot of the solution displacement process. In this design, efforts have been made to minimize the effects of electrolysis, Joule heating and undesired pressure driven flow on the measurements. An improvement on the current–time slope analysis is also presented. The Y-channel design was validated by comparing zeta potential measurements to published results. The zeta potential of several biological buffers relevant to the microfluidic community in plasma treated PDMS/PDMS and PDMS/Glass microchannels are presented. Preliminary studies of surface conductivity measurements using the Y-channel design were also conducted and are briefly discussed.     

Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.     

A robust test of uncertain linear systems

In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov＇s polynomials. Furthermore, for higher-order systems such as n ≥ 5, the usual four Kharitonov＇s polynomials need not be tested initially for sufficient condition of perturbed systems; rather, the necessary condition can be checked before going for sufficient condition. In order to show the effectiveness of the proposed method, numerical examples are shown and computational efficiency is highlighted.     

Collective motion in non-reciprocal swarms

This paper studies a non-reciprocal swarm model that consists of a group of mobile autonomous agents with an attraction-repulsion function governing the interaction of the agents. The function is chosen to have infinitely large values of repulsion for vanishing distance between two agents so as to avoid occurrence of collision. It is shown analytically that under the detailed balance condition in coupling weights, all the agents will aggregate and eventually form a cohesive cluster of finite size around the weighted center of the swarm in a finite time. Moreover, the swarm system is completely stable, namely, the motion of all agents converge to the set of equilibrium points. For the general case of non-reciprocal swarms without the detailed balance condition, numerical simulations show that more complex self-organized oscillations can emerge in the swarms. The effect of noise on collective dynamics of the swarm is also examined with a white Gaussian noise model.