a general class of sliding surface for sliding mode control in the conventional sliding mode control the relative degree of the chosen sliding surface is usually one this paper addresses a general class of sliding surface whose relative degree is no longer restricted to one we show that when the relative degree is more than two it is inevitable that there will exist a limit cycle for the nonlinear sign function and for the case of relative degree two the system possesses poor phase margin however these disadvantages can be remedied remarkably by smoothing out the control nonlinearity in a suitable boundary layer with a saturation function that ensures asymptotic stability of the overall system

design of variable structure controllers with continuous switching control a modified variable structure controller is proposed to deal with the conirol chattering problem which is one of the major difficulties for implementing the variable structure control vsc the new control strategy is effective for a class of uncertain nonlinear dynamical systems based on a suitably designed sliding sector a continuous switching controller whose control structure is switched whereas the control signal at switching remains continuous is constructed the complete attractiveness and the stability properties of the sliding sector in the sense of lyapunov stability ensure the retention of benefits achieved with the conventional vsc some typical examples are also investigated which show the improvement of system performance

brief paper output feedback variable structure control design with an h2 performance bound constraint in this paper we give an lmi based method for designing an output feedback variable structure control vsc system with an h 2 constraint the uncertain system model under consideration may have nonmatching disturbance input signals nonmatching disturbance input signal reduction is performed via h 2 norm minimization in terms of a constrained riccati inequality we give a sufficient condition for the existence of a linear sliding surface and a compensator guaranteeing an h 2 constraint and we show that the control parameters can be characterized by using the solution to the given inequality condition we also give a simple lmi based design algorithm of an output feedback vsc law guaranteeing an h 2 constraint finally by using a design example we show that our method can supplement the existing results

sufficient or necessary conditions for modal controllability and observability of roesser s 2 d system model controllability and observability properties of roesser s 2 d system model have been investigated and some strong necessary and or sufficient conditions are found

brief paper output feedback variable structure control for linear systems with uncertainties and disturbances this paper proposes a dynamic output feedback variable structure controller for linear mimo systems with mismatched and matched norm bounded uncertainties and matched nonlinear disturbances the proposed controller consists of nonlinear and linear parts similar to the unit vector type of controller the nonlinear part of the new controller takes care only of matched uncertainties and disturbances and on the other hand the linear part with full dynamics completely handles mismatched uncertainties designing such a linear part leads to use a lyapunov function associated with the full states which achieves the global stability against the mismatched uncertainties the resulting criteria are furthermore converted into solvable ones by using the so called cone complementary linearization algorithm for bi convex problems

output feedback control based on a high order sliding manifold approach in this note we address the problem of output feedback control of multiple input multiple output plants the proposed approach is based on a high order sliding manifold strategy the resulting controller exhibits strong robustness properties similar to high gain control laws but avoids peaking phenomena thanks to the adoption of a time varying sliding surface moreover the dynamic control law is continuous and differentiable thus avoiding chattering problems

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

analysis and design of variable structure systems using a geometric approach multivariable variable structure systems in the sliding mode are studies using a geometric approach the properties of system order reduction and disturbance rejection are proved using projector theory new design methods for the choice of switching hyperplanes are derived for the closed loop eigenvalue eigenvector assignment problem

reconstructing sliding surfaces for siso variable structure output feedback control systems using inverse method there exists a dynamic mapping relationship between the sliding variable and the output variable in a linear time invariant lti single input single output siso system this relationship is invariant of the matched disturbances which lies in the control space in this note a continuous time dynamic inverse compensator is proposed to reconstruct the sliding variable from the system output this inverse compensator is stable and causal provided that the original siso system is minimum phase and that the input output relative degree is less than or equal to one in case the system relative degree is greater than one a digital approximation for the inverse compensator is introduced to track the sliding variable in discrete time to the accuracy of o t where t is the sampling period thus the discrete time variable structure control vsc law can be implemented without full state accessibility

an efficient subspace method for the blind identification of multichannel fir systems we present a novel method for the blind identification of linear single input multiple output simo finite impulse response fir systems based on second order statistics our approach called the truncated transfer matrix method ttm proceeds in two major steps first the svd analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second the block toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations the proposed ttm method is analytical no optimization procedure involved and it is robust to noise we find that the method comes with an increased computational cost but it significantly outperforms state of the art second order methods in low signal to noise ratio snr situations

numerical methods to design the reaching phase of output feedback variable structure control abstract two numerical methods are developed to design a variable structure control that satisfies the reaching condition using static output feedback the design is formulated as a nonsmooth convex optimization problem for which existing algorithms are available it is shown how the resulting control law can be modified to be robust in the presence of parameter uncertainty or a disturbance numerical examples successfully demonstrate the developed techniques

discrete time output feedback sliding mode control design for uncertain systems using linear matrix inequalities an output feedback based sliding mode control design methodology for discrete time systems is considered in this article in previous work it has been shown that by identifying a minimal set of current and past outputs an augmented system can be obtained which permits the design of a sliding surface based upon output information only if the invariant zeros of this augmented system are stable in this work a procedure for realising discrete time controllers via a particular set of extended outputs is presented for non square systems with uncertainties this method is applicable when unstable invariant zeros are present in the original system the conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given a procedure to obtain a lyapunov matrix which simultaneously satisfies both a riccati inequality and a structural constraint is used to formulate the corresponding control to solve the reachability problem a numerical method using linear matrix inequalities is suggested to obtain the lyapunov matrix finally the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

stable robust tracking by sliding mode control sliding mode control is examined from the perspective of obtaining stable and robust tracking of an arbitrary time varying reference by a multi input output linear time invariant system driven by a certain class of bounded errors nonlinearities and disturbances most existing schemes for such systems are subsumed by the one presented here the results are developed via the use of inverse models and make clear the constraints imposed by the finite and infinite zero structure of the system in particular stable and robust tracking is shown to be obtained by the scheme in this paper if and only if the system is minimum phase

output feedback sliding mode control for sampled data systems we address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type by taking into account the disturbance compensation a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances in the framework of singular perturbation analysis it is shown that the closed loop system exhibits good robustness against exogenous disturbances

on variable structure output feedback controllers for uncertain dynamic systems a class of variable structure output feedback controllers for uncertain dynamic systems with bounded uncertainties is proposed no statistical information about the uncertain elements is assumed a variable structure systems approach and a geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed controllers

output feedback stabilization of uncertain plants a variable structure systems approach the problem of output stabilization for uncertain s1so systems is considered using structural transformations uncertain systems can change to the form convenient for output feedback design synthesis of observer based variable structure control for asymptotical stabilization or uniform ultimate boundedness of the closed loop system is provided examples are considered and simulation results are given

blind identification of digital communication channels with correlated noise blind identification consists of estimating the impulse response of a linear time invariant channel used for transmission of digital data by observing the channel output without knowledge of the transmitted symbol sequence we show how a previously proposed algorithm moulines et al 1995 based on second order statistics of the received signal can be modified to account for correlated noise

on variable structure output feedback controllers in a recent work by zak hui 1993 a sliding mode controller for mimo systems using static output feedback was proposed very nice geometric conditions for how to design sliding surfaces were given however there are two restrictive assumptions in it one is that the uncertainties in the system must be bounded by a known function of outputs which excludes some possible uncertainties in the a matrix if the system is described by the triple a b c the other one requires a matrix equality to be held which may also be very difficult to satisfy in many systems in this paper we propose a modification of the sliding mode controller for a class of single input single output siso systems which can eliminate the above mentioned limitations and under certain conditions guarantee global closed loop stability hence the range of applicability of zak hui s method can be greatly broadened

a transformed lure problem for sliding mode control and chattering reduction the sliding mode control problem is investigated with the frequency domain approach the authors show that the sliding mode control can be transformed into a lure problem with this formulation it is shown that the conventional sliding mode control with a nonlinear sign function can only guarantee to make the overall system stable but not asymptotically stable the authors also consider a practical situation where the sign nonlinearity may contain a hysteresis loop for this situation they show that even if the hysteresis loop is very small there still exists a limit cycle however chattering phenomenon caused by the limit cycle behavior can be eliminated by a certain class of nonlinearities

an ilmi approach to robust static output feedback sliding mode control this paper proposes a systematic methodology for designing robust static output feedback sliding mode control sofsmc for a class of systems with mismatched uncertainties this methodology consists of two parts one is a new sufficient and necessary condition for the existence problem in terms of two matrix inequalities the other is a direct solving method using the iterative linear matrix inequality ilmi technique the main advantages of this method are that only original system parameters are involved without any extra coordinate changes and that appealing to solving the static output feedback stabilization sofs problem is no longer required in addition the ilmi algorithm includes an optimal part to avoid high control efforts a numerical example also demonstrates the efficacy of the proposed approach