Electrical and Electronic Engineering - Research Publications
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ItemStability properties of reset systems(Elsevier, 2005-01-01)Stability properties for a class of reset systems, such as systems containing a Clegg integrator, are investigated. We present Lyapunov based results for verifying L2 and exponential stability of reset systems. Our results generalize the available results in the literature and can be easily modified to cover Lp stability for arbitrary p ∈ [1;∞]. Several examples illustrate that introducing resets in a linear system may reduce the L2 gain if the reset controller parameters are carefully tuned.
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ItemNonlinear sampled-data observer design via approximate discrete-time models and emulation(International Federation of Automatic Control, 2005)We study observer design for sampled-data nonlinear systems using two approaches: (i) the observer is designed via an approximate discrete-time model of the plant; (ii) the observer is designed based on the continuous-time plant model and then discretized for sampled-data implementation (emulation). In each case we present Lyapunov conditions under which the observer design guarantees semiglobal practical convergence for the unknown exact discrete-time model. The semiglobal region of attraction is expanded by decreasing the sampling period. The practical convergence set is shrunk by decreasing either the sampling period, or a modelling parameter which refines the accuracy of the approximate model.
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ItemNONLINEAR SAMPLED DATA CONTROLLER REDESIGN VIA LYAPUNOV FUNCTIONS(Elsevier BV, 2005)We provide results for redesign of Lyapunov function based continuous time controllers for sampled-data implementation, using a particular form of the redesigned controller and the Taylor expansion of the sampled-data Lyapunov difference. We develop two types of redesigned controllers that (i) make the lower order terms (in T) in the series expansion of the Lyapunov difference with the redesigned controller more negative and (ii) make the terms in the Taylor expansions of the Lyapunov difference for the sampled-data system with the redesigned controller behave as close as possible to the respective values of the continuous-time system with the original controller. Simulation studies illustrate the performance of our controllers.
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ItemNonlinear sampled-data observer design via approximate discrete-time models and emulation(Elsevier, 2005-01-01)We study observer design for sampled-data nonlinear systems using two approaches: (i) the observer is designed via an approximate discrete-time model of the plant; (ii) the observer is designed based on the continuous-time plant model and then discretized for sampled-data implementation (emulation). in each case we present Lyapunov conditions under which the observer design guarantees semiglobal practical convergence for the unknown exact discrete-time model. The semiglobal region of attraction is expanded by decreasing the sampling period. The practical convergence set is shrunk by decreasing either the sampling period, or a modelling parameter which refines the accuracy of the approximate model.
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ItemSummation-type conditions for uniform asymptotic convergence in discrete-time systems:: applications in identification(IEEE, 2005)We establish summation-type conditions to ensure the uniform convergence of discrete-time systems, parameterized in the sampling time. The main results are analogous to previous results obtained in the domain of continuous-time systems and that we have referred to as "integral conditions". The sufficient conditions that we present here can also be interpreted as conditions for convergence of series. Our main results are also useful for design of sampled-data controllers via approximate models; for illustration, we present two results on control design reminiscent of common problems arising in identification and adaptive control.
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ItemInput-output stability of wireless networked control systems(IEEE, 2005-01-01)This paper provides a general framework for analyzing the stability of general nonlinear networked control systems (NCS) with disturbances in the setting of ℒp stability. With general, weak sufficient conditions on the NCS, we are able to conclude much tighter performance bounds than [1] and [2] for a very wide class of NCS. We also define the notion of persistently exciting (PE) scheduling protocols, discuss how PE leads to ℒp stability for high enough transmission rates and show that PE is a natural property to demand, especially in the design of wireless scheduling protocols. Our results are of wide applicability as the analyses require neither the existence nor explicit construction of Lyapunov functions and the performance and stability bounds are completely parameterized by properties of the "network-free" system and a single NCS parameter chosen in the design of the scheduling protocol.
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ItemLyapunov functions for time varying systems satisfying generalized conditions of Matrosov theorem(IEEE, 2005-01-01)The classical Matrosov theorem concludes uniform asymptotic stability of time varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semi-definite derivative along solutions) and another auxiliary function with derivative that is strictly non-zero where the derivative of the Lyapunov function is zero [10]. Recently, several generalizations of the classical Matrosov theorem that use a finite number of Lyapunov-like functions have been reported in [5]. None of these results provides a construction of a strong Lyapunov function (positive definite, decrescent, with negative definite derivative along solutions) that is a very useful analysis and controller design tool for nonlinear systems. Inspired by generalized Matrosov conditions in [5], we provide a construction of a strong Lyapunov function via an appropriate weak Lyapunov function and a set of Lyapunov-like functions whose derivatives along solutions of the system satisfy a particular triangular structure. Our results will be very useful in a range of situations where strong Lyapunov functions are needed, such as robustness analysis and Lyapunov function based controller redesign.
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ItemA small-gain approach to stability analysis of hybrid systems(IEEE, 2005-01-01)We propose to use ISS small-gain theorems to analyze stability of hybrid systems. We demonstrate that the small-gain analysis framework is very naturally and generally applicable in the context of hybrid systems, and thus has a potential to be useful in many applications. The main idea is illustrated on specific problems in the context of control with limited information, where it is shown to provide novel interpretations, powerful extensions, and a more unified treatment of several previously available results. The reader does not need to be familiar with ISS or small-gain theorems to be able to follow the paper.
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ItemPractical encoders for controlling nonlinear systems under communication constraints(IEEE, 2005-01-01)We introduce a new class of dynamic encoders for continuous-time nonlinear control systems which update their parameters only at discrete times. We prove that the information reconstructed from the encoded feedback can be used to deliver a piece-wise constant control law which yields semi-global practical stability. The result is achieved by assuming a property weaker than asymptotic stabilizability.
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ItemInput-to-state stabilization of linear systems with quantized feedback(IEEE, 2005-01-01)We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in". Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time, while the second one incorporates time sampling. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work.