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 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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ItemNetworked control systems: An emulation approach to controller design(Elsevier BV, 2007-01-01)We overview our recent work on a design approach for networked control systems (NCS) that resembles controller emulation for sampled-data systems. In the first step, we design a controller ignoring the network and, in the second step, we implement the designed controller over the network with sufficiently fast transmissions and a given protocol. Our results have several features: (i) they apply to general nonlinear systems with disturbances; (ii) we obtain explicit (often non-conservative) bounds on the maximal allowable transmission interval that guarantee stability; (iii) and we show that this approach is valid for a wide range of network scheduling protocols. This provides a flexible framework for design of NCS that is amenable to various extensions and modifications, such as a treatment of dropouts and stochastic protocols, combined controller/protocol design for linear plants, and so on.
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ItemInput-to-state stability analysis via averaging for parameterized discrete-time systems(Watam Press, 2010-12-15)The paper studies semi-global practical input-to-state stability (SGP-ISS) of a parameterized family of discrete-time systems that may arise when an approximate discrete-time model of a sampled-data system with disturbances is used for controller design. It is shown under appropriate conditions that if the solutions of the time varying family of discrete-time systems with disturbances converge uniformly on compact time intervals to the solutions of the average family of discrete-time systems, then ISS of the average family of systems implies SGP-ISS of the original family of systems. A trajectory based approach is utilized to establish the main result.
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ItemAveraging for a class of hybrid systems(Watam Press, 2010-12-15)Averaging theory for ordinary differential equations is extended to a class of hybrid systems. Rapid time variations in the flow map of a hybrid system generate solutions that are also solutions of a slightly perturbed time-invariant average hybrid system. Results relating solutions of the time-varying system to solutions of the average system ensue. In the absence of finite escape times for the average system, on compact time domains each solution of the time-varying system is close to a solution of the average system. If the average system is asymptotically stable, the time-varying system exhibits semi-global, practical asymptotic stability. These results rely on mild regularity properties for the average system. In particular, the average system is not required to exhibit unique solutions. Both periodic and non-periodic flow maps are considered. The results are partially motivated by the desire to justify a pulse-width modulated implementation of hybrid feedback control for nonlinear systems.
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ItemNetworked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010-08-01)There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.
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ItemRobustness of nonlinear control systems with quantized feedback(ELSEVIER SCI LTD, 2010-05-01)This paper analyzes the stability of nonlinear systems with quantized feedback in the presence of exogenous disturbances. This paper is an extension of [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Trans. Automat. Control 52 (2007), 413-436] to nonlinear systems. Under appropriate assumptions using a nonlinear modification of the scheme proposed in [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Transactions on Automat. Control 52 (2007), 413-436], it is shown here that it is possible to achieve input-to-state and nonlinear gain l 2 stability for nonlinear systems with quantized feedback.
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ItemInput-to-State Stability and Averaging of Linear Fast Switching Systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010-05-01)We consider the averaging method for stability of rapidly switching linear systems with disturbances. We show that the notions of strong and weak averages proposed in [1], with partial strong average defined in this note, play an important role in the context of switched systems. Using these notions of average, we show that exponential input-to-state stability (ISS) of the strong and the partial strong average system with linear gain imply exponential ISS with linear gain of the actual system. Similarly, exponential ISS of the weak average guarantees an appropriate exponential derivative ISS (DISS) property for the actual system. Moreover, using the Lyapunov method, we show that linear ISS gains of the actual system and its average converge to each other as the switching rate is increased.
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ItemSummability characterizations of uniform exponential and asymptotic stability of sets for difference inclusions(TAYLOR & FRANCIS LTD, 2010-01-01)We present several equivalent characterizations of uniform global exponential stability (UGES) and uniform global asymptotic stability (UGAS) of arbitrary closed (not necessarily compact) sets for non-linear difference inclusions. In particular, we provide several characterizations of these stability properties via summability criteria that do not require the knowledge of a Lyapunov function. We apply our results to prove novel-nested Matrosov theorems for UGES and UGAS of the origin for time-varying non-linear difference inclusions.