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In this study, the problem of cooperative fault accommodation in formation flight of unmanned vehicles represented by linear time-invariant models that are subject to loss-of-effectiveness actuator faults is investigated through a hierarchical framework. Three hierarchical levels are envisaged, namely a low-level fault recovery (LLFR), a formation-level fault recovery and a high-level supervisor. In the LLFR module, a recovery controller is designed by using an estimate of the actuator fault. A performance monitoring module is then introduced at the high-level to identify a 'partially low-level recovered' vehicle because of inaccuracy in the fault severity estimate that results in violating the 'error specification' of the formation mission. The high-level supervisor then activates the formation-level fault recovery module to compensate for the resulting performance degradations of the partially low-level (LL) recovered vehicle at the expense of other healthy vehicles. The fault is accommodated by reconfiguring the formation structure through the novel notion of the weighted absolute measurement formation digraph, activating a robust controller for the partially LL recovered vehicle, and imposing a constraint on the desired input signals. Numerical simulations for a formation flight of five satellites in the planetary orbital environment are presented to confirm the validity and effectiveness of the proposed analytical work. [ABSTRACT FROM AUTHOR]

In this study, an attempt has been made to design an output feedback controller for local stabilisation of uncertain linear time-invariant plant with bounded control inputs. The design is accomplished via parametric H∞ loop-shaping control by describing the uncertainty as perturbations to normalised coprime factors of the shaped plant. The shaped plant is designed based on the closed-loop design specifications by appropriately choosing the weighting transfer function matrices. For the existence of stabilising controller, a set of sufficient conditions has been derived in linear matrix inequality framework and subsequently, a region of attraction is estimated such that the control inputs never exceed the pre-specified bounds. To illustrate the effectiveness of the proposed method, a numerical example has been elucidated. [ABSTRACT FROM AUTHOR]

This study achieves superior multi-channel output gain margin (MOGM), compensation of continuous-time, linear time-invariant (LTI), non-minimum-phase, unstable, multi-input-multi-output (MIMO) plants by first input-output decoupling these in open-loop and then effecting zero placements of the decoupled loops using single-input-single-output (SISO) periodic feedback. The condition that allows this controller to yield arbitrarily large MOGM is also found out. An example is considered to illustrate the design procedure and the capability of this controller. [ABSTRACT FROM AUTHOR]

This study presents an eigenvalue assignment control architecture for a class of linear time-varying (LTV) systems in the presence of time-varying disturbances. Eigenvalue assignment architecture is presented as a way to achieve feedback stabilisation for LTV disturbed systems. With an input compensator design, the output of slowly LTV systems with disturbances can practically track the reference. Moreover, the implementation of the proposed eigenvalue assignment technique in practice has been demonstrated by using adaptive estimation of time-varying disturbances. [ABSTRACT FROM AUTHOR]

This study investigates the problem of observer-based control for linear time-invariant system with limited communication capacity. The system states are unavailable and the system outputs are subject to logarithmic quantisation, which can be regarded as outputs with disturbances. Traditional Luenberger observers and proportional and derivative observers are not effective to deal with such kind of estimation problems. A new estimation technique to cope with discontinuous quantised outputs is proposed such that the estimation of system states and quantisation error can be obtained simultaneously. In this design, the state variables of the derived error system are discontinuous at quantisation switching times, and traditional Lyapunov function cannot be used to perform the stability analysis. Hence, a new time-dependent Lyapunov functional and a generalised Newton-Leibniz formula are proposed to deal with this difficulty. A sufficient condition for the stability analysis of the error dynamics is established and an observer-based control scheme is proposed to stabilise the plant. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed technique. [ABSTRACT FROM AUTHOR]

This study aims at developing new linear matrix inequality (LMI) conditions for robust D-stability and D-stabilisation of linear time-invariant uncertain systems in polytopic domains. An existing LMI condition for robust D-stability is lifted into those of larger dimensions that are given as functions of a certain integer κ. Based on the consequent conditions, new sufficient conditions for the existence of a state-feedback control law ensuring the robust D-stability of the closed-loop system is proposed in terms of LMIs. Finally, examples are given to illustrate the benefit of the proposed methods. [ABSTRACT FROM AUTHOR]

This study presents an online motion planning algorithm for generating reference trajectories during flight phases of a planar monopedal robot to transfer the configuration of the mechanical system from a specified initial pose to a specified final one. The algorithm developed in this research is based on the reachability and optimal control formulations of a time-varying linear system with input and state constraints. A two-level control scheme is developed for asymptotic stabilisation of a desired period-one orbit during running of the robot. Within-stride controllers, including stance and flight phase controllers, are employed at the first level. The flight phase controller is a feedback law to track the reference trajectories generated by the proposed algorithm. To reduce the dimension of the full-order model of running, the stance phase controller is chosen to be a parameterised time-invariant feedback law that produces a family of two-dimensional finite-time attractive and invariant submanifolds. At the second level, the parameters of the stance phase controller are updated by an event-based update law to achieve hybrid invariance and stabilisation. To illustrate the analytical results developed for the behaviour of the closed-loop system, a detailed numerical example is presented. [ABSTRACT FROM AUTHOR]

In this study a recent result on the quadratic stability of switched linear time-invariant systems is applied to the problem of vehicle rollover prevention based on selectively switching between two suspension settings. The suggested switching control scheme reduces the transient magnitude of the load transfer ratio (LTR), which is the rollover detection metric, when and if it is above a certain threshold by switching to a stiffer suspension setting from a default soft one. In this way, the controller activates only when the potential for rollover is significant as measured by the LTR. The switching suspension parameters are chosen in a way that results in closed-loop switched roll dynamic response that is guaranteed to be quadratically stable under arbitrary switching. Moreover, a spectral condition is given that allows checking the stability of the switched roll dynamics that is subject to actuator uncertainty when the upper and lower bounds of the uncertain parameters are known. Numerical simulations demonstrate the efficacy of the suggested switched control approach. [ABSTRACT FROM AUTHOR]

Fixed parameter iterative learning control (ILC) for linear-time invariant, single-input single-output systems subject to output noise is analysed with the intent of predicting the expectation of the underlying 'noise-free' mean square error (Euclidean norm) of the time series on each iteration. Explicit formulae are obtained in terms of the 'lifted' matrix models of the plant. Computational experiments are used to confirm the correctness of the proposed properties. Finally, frequency domain formulae are derived to provide insight into links between plant characteristics, noise spectra and other ILC parameters, and illustrated by application to the inverse-model-based ILC algorithm. [ABSTRACT FROM AUTHOR]

In this study the swarm stability problem of high-order linear time-invariant (LTI) swarm systems with directed graph topology is dealt with. Consensus can be regarded as a specific type of swarm stability problem. Necessary and sufficient conditions for both swarm stability and consensus are presented. These conditions depend on the graph topology, the dynamics of agents and the interactions among the neighbours. Simulation instances are shown to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This article studies the problems of stability analysis and controllers design for continuous-time linear systems with the consideration of full state saturation as well as partial state saturation. Owing to the difficulty and complexity in the controller design under state saturation, a new and tractable system is constructed, and it is shown that the constructed system is with the same domain of attraction as the original system. Based on this property, an linear matrix inequality (LMI) based method is presented for estimating the attraction domain of the origin for the new constructed system with state saturation. In addition, an algorithm is developed for designing dynamic output-feedback controllers, which guarantee that the attraction domain of the origin for the closed-loop system is as 'large' as possible. An example is given to illustrate the effectiveness of the design method. [ABSTRACT FROM AUTHOR]

The authors study the consensus problem in networked non-holonomic systems (NHSs). Based on Brockett's stabilisability condition, the stabilisation of NHSs is usually considered by using time-varying or discontinuous control (including switching control). Observing that the consensus problem has more flexibility than the stabilisation one, the authors aim to establish time-invariant continuous state feedbacks for the problem at hand. [ABSTRACT FROM AUTHOR]

In this study, the problem of finite-time stability of linear time-varying singular systems with impulses at fixed times is addressed. Sufficient conditions for linear singular impulsive systems to be finite-time stable are proposed in terms of a set of coupled matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the static output-feedback stabilisation problem of discrete-time networked control systems. If the controlled plant is a discrete-time system, the networked control system with time-varying network-induced delays and data packet dropouts in the transmission is modelled as a discrete-time system with time-varying delays in the state. The network-induced delays are assumed to have both an upper bound and a lower bound. Next, an asymptotic stability condition for the networked control systems is established, which depends on the upper and lower bounds of delay times. Then, three approaches to the static output-feedback controller are proposed, where the effect of both network-induced delays and data packet dropouts has been considered. Furthermore, the robust stability condition and controller design method for such networked control systems with structured uncertainties are presented. All the results are formulated in the terms of linear matrix inequalities (LMIs), which are numerically very efficiently solved via LMI toolbox in the Matlab. Finally, three examples are worked out to illustrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of estimating feasible parameter sets for linear discrete-time systems with unknown-but-bounded noise is investigated. Considering that the feasible parameter set of a linear discrete-time system with bounded noise is a convex polytope and that a convex polytope can be triangulated into a limited number of simplexes with good properties, the authors propose an exact triangulation description method for the feasible parameter set. A convex polytope triangulation algorithm is introduced and a recursive algorithm of estimating the feasible parameter set in correspondence with the system description is developed. Simulation examples show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

By phase plane partitioning, dynamics of individual generators in multimachine systems are approximately represented by means of a sequence of linear time-invariant (LTI) state-space equations, based on which various static VAR compensators (SVCs) are designed to stabilise the individual generators by exploiting the well-known LTI stabilisation techniques. More precisely, the author works out state-feedback-controlled SVCs through pole assignment (PA) and least quadratic regulation (LQR), respectively. The suggested SVCs can also accommodate transient and steady-state performance specification on the generator's dynamics, besides its stabilisation. Numeric examples clearly illustrate efficacy and convenience of the stabilisation techniques. [ABSTRACT FROM AUTHOR]

The controllability problem of high-order linear time-invariant (LTI) continuous-time swarm systems is investigated. A necessary and sufficient condition for complete controllability of homogeneous swarm systems is given. The controllability of graph is important and is analysed in detail. The concept of formation controllability is proposed and the relationship between complete controllability and formation controllability is studied. [ABSTRACT FROM AUTHOR]

In this study, the problem of designing regular robust l2–l∞ filter for a class of linear singular discrete-time systems with norm-bounded uncertainties is investigated. A class of regular linear filters is fully analysed, then necessary and sufficient conditions of robust admissibility are established. Guaranteed l2–l∞ performance of the filtered system is provided and expressed in terms of the solution of strict linear matrix inequalities (LMIs). The cases of full- and zeroth-order realisable filter are derived as limiting cases of design. Numerical examples are worked out to illustrate the theoretical development. [ABSTRACT FROM AUTHOR]

This study presents a partial-parallel decoder architecture for π-rotation low-density parity-check (LDPC) codes, which have regular rotation structure and linear time encoding architecture. One improved construction method, which deletes one parity-check bit corresponding to the actually redundant weight-1 column, is proposed, and then an effective encoding algorithm, which utilises only the index of one permutation sub-matrix, is presented. Based on the group-structured and permutation characteristics, two-dimensional arrays are used to store the check/variable node information during iterations, and then a cycle reuse mapping architecture is proposed for messages passing among memories, bit functional units (BFUs) and check function units (CFUs). Partial-parallel decoder with this mapping architecture is reconfigurable by only changing four mapping patterns, and needs no address generators which exist in some architecture-aware (AA) LDPC decoders, such as quasi-cyclic LDPC (QC-LDPC) decoders. Simulation results show that the proposed methods are feasible and effective. [ABSTRACT FROM AUTHOR]

Controllability and observability at infinity of linear time-varying descriptor systems are considered. New characterisations of controllability and observability at infinity are given. Based on the definitions of controllability and observability at infinity, necessary and sufficient conditions for these properties are obtained and presented in terms of original system parameters. The present framework is shown to overcome several difficulties inherent in other treatments of descriptor systems. [ABSTRACT FROM AUTHOR]

This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

This study presents a dynamic post-filtering approach to a single-input-single-output sampled-data variable structure output feedback control problem. Given a sliding surface, Σ(x)=0 (x being the system state vector), designed through standard procedures with the assumption of full state accessibility, a dynamic filter, denoted post-filter, is employed to synthesise Σ(x) by means of output variable alone. In contrast with a state observer, the post-filter is invariant of the matched disturbances; and it requires only partial information of the system parameters. Thus, the robustness property of the variable structure system is retained. Let T be the sampling period. A sampled-data realisation of the post-filter is done by zero-order hold. Depending on the system relative degree, either Σk or Σk-1 can be obtained for implementing the variable structure control law. A discrete-time switching-type control law, which is originally designed to satisfy the continuous-time reaching condition, will lead to a quasi-sliding motion, forming a boundary layer of thickness O(T) about the sliding surface. The stability of the post-filter is ensured if the system output is in minimum phase and that the sliding mode dynamics are chosen properly. [ABSTRACT FROM AUTHOR]

This paper studies the simultaneous fault detection and control problem for linear uncertain discrete-time systems. A design procedure dealing with polytopic uncertainties is proposed for residual generation, where both the fault detection objectives and some control objectives are considered simultaneously through certain performance indexes. To cope with the fault sensitivity performance index in a given frequency range directly, the generalised KYP lemma is introduced in this framework. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

A type of proportional-integral observers for discrete-time linear systems is proposed. Based on a complete parametric solution to the generalised Sylvester matrix equation, a parametric design approach for such a type of observers is proposed. The proposed approach provides all the gain matrices of the observer, gives the parametric expression for the corresponding finite left eigenvector matrix of the observer system matrix and guarantees the regularity of the observer system. A numerical example is provided to show the design procedure and illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Based on the satisfactory fault-tolerant control strategy, the problem of reliable guaranteed cost control with multiple criteria constraints is investigated for a class of uncertain discrete-time systems subject to sensor faults. The state-feedback controller is developed by linear matrix inequalities approach such that, for all admissible parameters uncertainties and possible sensor faults, the given upper bounds on the amplitudes of control input signals be ensured, all the closed-loop poles be placed into the pre-specified regional disk, and the expected quadratic cost performance index as well as the given H∞ norm index of disturbance rejection level be guaranteed, simultaneously. Thus, with the above multiple criteria constraints, the resulting closed-loop system can provide satisfactory stability, transient property, external disturbance attenuation level and quadratic cost performance, despite the possible sensor faults. [ABSTRACT FROM AUTHOR]

A kind of new linear matrix inequality (LMI)-based formulation is presented for multi-objective H∞/α-stability controller synthesis of linear time invariant (LTI) systems. New LMI-based conditions enable to parameterise controllers without involving the Lyapunov variables in the formulation. With this feature, multi-objective controllers can be designed, with non-common Lyapunov variables and two additional adjustable scalars. Furthermore, to find the minimum possible cost, LMI-based conditions can be solved by the grid of the space which is composed of these scalars. When compared with previous results based on a common Lyapunov function, this provides less conservative results. Finally, two numerical examples are included to illustrate the effectiveness of the proposals. [ABSTRACT FROM AUTHOR]

The methodology for the nonlinear modelling and analysis of active magnetic bearing (AMB) systems in the harmonic domain (HD) is presented. This approach is based on the HD linearisation of the AMB system around nonlinear stationary solutions at different rotating speeds. The main advantage obtained is the representation of the periodic LTV models that describe the steady-state dynamics for each speed, by means of LTI models in the HD. In order to show its possibilities, the proposed approach is applied to an AMB laboratory testbed based on the MBC500 Rotor Dynamics from Launchpoint Technologies. This analysis explains the nonlinear nature of the response that appears at high speeds, due to the large oscillations introduced by the shaft unbalance, and detects a low-frequency gain loss when increasing the rotating speed. This phenomenon causes the instability of the system, leading to destructive crashes. In addition, the analysis allows to take into account the effect of the delay introduced by the calculation time in the system behaviour when the controller is implemented by using digital devices. [ABSTRACT FROM AUTHOR]

Issues of observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay and disturbance input are addressed, where the Lipschitz condition is expressed in a componentwise rather than aggregated manner. It has been shown that both full-order and reduced-order robust H∞ observers can be obtained by means of the same convex optimisation procedure with minimisation of the disturbance attenuation upper bound γ>0. It is also shown that for a prescribed H∞-norm upper bound γ>0, the tolerable Lipschitz bounds can be obtained by another convex optimisation procedure. A numerical example is presented to show the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

The problem of robust l2–l∞ filtering for switched linear discrete-time systems with polytopic uncertainties and time-varying delays is investigated. The time delay is assumed to be time-varying and bounded, which covers constant delay and mode-dependent constant delays as special cases. A robust switched linear filter is designed based on the mode-switching idea and a parameter-dependent stability approach such that the corresponding filtering error system is robustly asymptotically stable and achieves a prescribed l2–l∞ performance index for all admissible uncertainties. The existence conditions for such a filter, dependent on the upper and lower bounds of time-varying delays, are formulated in terms of a set of linear matrix inequalities. By solving that corresponding convex optimisation problem, the desired filter is obtained and an optimal l2–l∞ noise-attenuation level bound of the resulting filtering error system is guaranteed as well. A numerical example is given to show the feasibility and potential of the theoretical results. [ABSTRACT FROM AUTHOR]

The problem of designing a resilient L2–L∞ filter for a class of linear uncertain state delay systems with uncertainties that belong to a convex-bounded polytopic domain is investigated. The objective is to derive tractable synthesis conditions for the resilient design of full-order and reduced-order filters such that a prescribed energy-to-peak disturbance-attenuation level is attained for all admissible uncertainties and gain perturbations. Both additive and multiplicative gain perturbations are considered. It is established that the filter design can be obtained from the solution of the convex optimisation problem over linear matrix inequalities. The design results are developed for both delay-independent and delay-dependent cases. In the latter case, two approaches are used: descriptor and extended Newton–Leibniz. Results on numerical simulations are presented to demonstrate the behaviour of the resilient filters. [ABSTRACT FROM AUTHOR]

An approach to compute the ℋ2- or ℋ∞-guaranteed costs with any prescribed accuracy is presented. The proposed approach can be applied to uncertain state–space models of linear time-invariant systems, where the system matrices depend on uncertain parameters or vary in a polytopic domain of the space of matrices. The developed approach is based on a new implementation of the branch-and-bound algorithm with the upper-bound functions based on linear matrix inequality (LMI) characterisations. The branch operation is based on a new subdivision technique that can be applied to any kind of polytope shape, not restricted to the hyper-rectangle case. When applied alone, the LMI-based analysis formulations can fail to compute the guaranteed costs, or they can present conservative results. Examples are presented to illustrate that the proposed analysis approach overcomes the problems faced with LMI-based formulations with reasonable computational time. [ABSTRACT FROM AUTHOR]

An integrated batch-to-batch control and within-batch online control strategy for tracking product quality trajectories in batch processes is proposed. On the basis of a batch-wise linear time-varying perturbation model, iterative learning control (ILC) is implemented for batch-to-batch control and the convergence of tracking errors under ILC is guaranteed. Within a batch, a predictive model is constructed by directly partitioning the linear time-varying model according to time, then batch model predictive control with shrinking horizons is applied online to reduce the effects of model-plant mismatch and/or unknown disturbances. By properly combining these two control methods, the integrated control strategy can complement both methods to obtain good performance. The proposed strategy is demonstrated on a simulated batch polymerisation process, and the results show that the performance can be improved quite significantly under the integrated control strategy than only under ILC, especially when disturbances occur. [ABSTRACT FROM AUTHOR]

The authors present an enhanced composite nonlinear feedback (CNF) control technique for discrete-time systems with input saturation and with external disturbances. The conventional CNF control is proven to be capable of yielding better transient performance in tracking control for systems with input saturation. However, when the given system has external disturbances as in most practical situations, the conventional CNF control yields some steady-state errors in the resulting output response. The enhanced CNF technique presented is an extension of the conventional one. It retains the good transient properties of the conventional CNF control and at the same time has the additional capacity for eliminating steady-state bias because of unknown constant disturbances. A numerical example and practical disk drive servo system design are provided to demonstrate the effectiveness of this control technique. Experimental results show that the new design yields a huge improvement over classical approaches. [ABSTRACT FROM AUTHOR]

The dynamic output feedback guaranteed cost control problem is investigated for a class of uncertain discrete-time systems with multiple time-varying state delays and norm-bounded parameter uncertainties. Attention is focused on the design of the dynamic output feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Delay-dependent sufficient conditions for the existence of the desired guaranteed cost controllers are derived without involving model transformation and bounding technique for cross terms, and these conditions are formulated in terms of nonlinear matrix inequalities. An iterative algorithm involving convex optimisations is presented to solve these nonlinear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The problem of the delay-dependent stability of linear systems with multiple time delays is discussed. A new method is first presented for a system with two time delays, in which free weighting matrices are used to express the relationships among the terms of the Leibniz–Newton formula. Next, this method is used to show the equivalence between a system with two identical time delays and a system with a single time delay. Then, a numerical example verifies that the criterion given is effective and is a significant improvement over the existing ones. Finally, the basic idea is extended to a system with multiple time delays. [ABSTRACT FROM AUTHOR]

The problem of sampled-data state reconstruction in linear time invariant systems is considered. A new full order observer structure that can generate intersample state estimation is introduced. The observer synthesis is carried out using the H∞ framework and is shown to have some important advantages over the classical lifting technique that has been used to study similar problems. A simulation example illustrates the application of the proposed design in the fast rate fault detection problem. [ABSTRACT FROM AUTHOR]

The two-dimensional (2-D) system theory iterative learning control (ILC) techniques for linear time-invariant discrete systems are extended to the cases of linear time-variant discrete systems. By exploiting the convergent property of 2-D linear time-variant discrete systems with only one independent variable, a kind of 2-D system theory ILC approach is presented for linear time-variant discrete systems. Sufficient conditions are given for convergence of the proposed ILC rules. Two numerical examples are used to validate the ILC procedures. [ABSTRACT FROM AUTHOR]

A computationally efficient linear matrix inequality (LMI)-based criterion for the global asymptotic stability of discrete-time systems in a state-space realisation with state saturation nonlinearities is presented. The criterion turns out to be an improved generalised version of a previously reported LMI-based criterion. The extension of the approach to a situation involving partial state saturation nonlinearities is performed. [ABSTRACT FROM AUTHOR]

The optimal updating law of the problem of optimal higher-order iterative learning control is given explicitly and the convergence of the tracking errors is proved. Two examples show that the convergence of the optimal higher-order iterative learning control is faster than that of the optimal one-order iterative learning control. [ABSTRACT FROM AUTHOR]

The conventional quasi-steady model of HVDC is not able to describe the dynamic switching behaviour of HVDC converters. By means of the sampled-data modelling approach, a linear time-invariant (LTI) small-signal dynamic model is developed for the HVDC main circuit in the synchronous rotating d-q reference frame. The linearised model is validated by time-domain simulation, and it can be seen that the model represents the dynamic response of the static switching circuits to perturbations in operating points. The model is valid for analysing oscillations including high frequency modes such as subsynchronous oscillation (SSO) and high frequency instability. The model is applied in two cases: (i) SSO analysis where the results are compared with the quasi-steady approach that has shown its validation for normal SSO analysis; (ii) high frequency eigenvalue analysis for HVDC benchmark system in which the results of root locus analysis and simulation shows that increased gain of rectifier DC PI controller may result in high-frequency oscillatory instability. [ABSTRACT FROM AUTHOR]

The restricted structure optimal deconvolution filtering, smoothing and prediction problem for multivariable, discrete-time linear signal processing problems is considered. A new class of discrete-time optimal linear estimators is introduced that directly minimises a minimum variance criterion but where the structure is prespecified to have a relatively simple form. The resulting estimator can be of much lower order than a Kalman or Wiener estimator and it minimises the estimation error variance, subject to the constraint referred to above. The numerical optimisation algorithm is simple to implement and the full-order optimal solutions are available as a by-product of the analysis. Moreover, the restricted structure solution may be used to compute both IIR and FIR estimators. A weighted H2 cost-function is minimised, where the dynamic weighting function can be chosen for robustness improvement. The signal and noise sources can be correlated and the signal channel dynamics can be included in the system model. The algorithm enables loworder optimal estimators to be computed that directly minimise the cost index. The main technical advance is in the pre-processing, which enables the expanded cost expression to be simplified considerably before the numerical solution is obtained. The optimisation provides a direct minimisation over the unknown parameters for the particular estimator structure chosen. This should provide advantages over the simple approximation of a high-order optimal estimator. The results are demonstrated in the estimation of a signal heavily contaminated by both coloured and white noise. [ABSTRACT FROM AUTHOR]

A matrix-analytic approach is applied to analyse both the long-term and the short-term drop behaviour of a router with an RED scheme. The bursty nature of packet drop is examined by means of conditional statistics with respect to alternating congested and non-congested periods. All of the four related performance measures are derived by conditional statistics, including the long- term drop probability, and the three short-term measures comprising average length of a congested period, average length of a non-congested period, and the conditional packet drop probability during a congested period. [ABSTRACT FROM AUTHOR]

A method of designing linear parameter varying (LPV) control systems based on the parameterisation of all quadratically stabilising controllers is presented. Conceptions of doubly coprime factorisation and Youla parameterisation of LTI systems are extended to LPV systems with respect to quadratic stability using a state space expression. The parameterisation of closed loop systems, which are affine with any quadratically stable Q-parameter, is then described. This description enables the application of the Q-parameter approach to a variety of LPV control system designs. Above all, a systematic H∞ strategy is focused on and a necessary and sufficient condition and also a design scheme of Q to obtain L2-gain performance, are clarified. [ABSTRACT FROM AUTHOR]

The design of a minimum variance regulator for systems operating in dynamical uncertain environments is considered. For minimum variance self-tuning control of an unknown linear time-invariant system, a stable control strategy is developed that improves the transient response by using multiple models to describe the different environments and switching between the relative controllers. The controller is determined at every time instant by the model which best approximates the plant. The performance of the controller is evaluated by a set of simulation tests. [ABSTRACT FROM AUTHOR]

The design of a repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented. Using a Lyapunov functional for the time-delay systems, a sufficient condition is derived in terms of either an algebraic Ricatti inequality or a linear matrix inequality (LMI), which ensures robust stability of the repetitive control system. Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint of the free parameter. [ABSTRACT FROM AUTHOR]

It is understood how to transform a linear periodically time-varying (LPTV) filter/difference equation into an equivalent multiple-input/multiple-output (MIMO) structure, or transfer matrix, with linear time-invariant (LTI) elements, but no published method exists for the reverse operation. The paper presents a technique to transform from the LTI MIMO structure to the original single-input/single-output LPTV difference equation and discusses its implications. In addition, it is shown how this new result is then used to represent parallel and cascade connections of LPTV systems as single LPTV filters, implement order reduction of an LPTV difference equation, and finally obtain an LPTV difference equation representation that is equivalent to an LPTV state-space structure. [ABSTRACT FROM AUTHOR]

Lower and upper bounds are given to calculate the smallest possible left-half-plane where all poles of a single-input single-output plant with no zeros can be stabilised using constant gain feedback. The results are expected to have immediate application areas in control system theory and filter design. [ABSTRACT FROM AUTHOR]