on undershoot and nonminimum phase zeros in this note we derive a simple necessary and sufficient condition for a stable system to exhibit an undershooting step response specifically we show that undershoot occurs if and only if the plant has an odd number of real right half plane zeros

the racah wigner approach to harmonic oscillations of the cluster of nodes of a cube the racah wigner approach is applied to demonstrate various group theoretic labelling schemes for modes of oscillations and elasticity parameters of the cluster of nodes of a cube it is shown that there exists a fundamental basis in the configuration space closed under the action of the group oh the geometric symmetry group of the equilibrium it provides a transparent interpretation of all basic invariants the fibre bundle and tensor product structure of invariant bilinear forms over the configuration space yields three classification schemes for elasticity parameters in a way that resembles racah recoupling of several angular momenta

a unified method for the design of nonovershooting linear multivariable state feedback tracking controllers we consider the use of linear multivariable feedback control to achieve a nonovershooting step response a method is given for designing a linear time invariant state feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time under some mild assumptions we present a unified design method that can be applied to continuous and discrete time systems square and non square systems minimum and nonminimum phase systems and also strictly proper and nonstrictly proper systems

the induction coefficient of induced representation theory its algebra and an analytic expression the induction coefficient is defined as the element of a matrix reducing the induced representation into irreducible constituents the authors give the algebra of these coefficients and a closed analytic expression in terms of matrix elements of coset representatives the consequences of this choice are derived and the importance of some of these results for the racah wigner coupling algebra of the symmetric and unitary groups noted

every stabilizing controller is l sub 1 and h sub infinity optimal a new formulation is given for the problem of optimally rejecting possibly unbounded disturbances it is shown that for a given plant every particular stabilizing controller is l sub 1 and also h sub infinity optimal for some particular classes of appropriately chosen disturbances an example demonstrates the authors work

minimization of a closed loop response to a fixed input for siso systems it is shown that the problem of minimizing a regulated response of a single input single output system due to a fixed bounded input can be converted via polynomial techniques to a linear infinite dimensional chebyshev data fitting problem approximating feasible solutions within any specified degree of accuracy can be obtained by converting the original problem into a sequence of increasingly large finite dimensional chebyshev approximation problems for which solution stable and efficient numerical methods exist a direct formula for calculating tight upper bounds to the approximation error is provided the link between the present algebraic approach and the dahleh and pearson functional analytic one 1988 is also discussed

minimization of a regulated response to a fixed input the problem of minimizing a regulated output due to a specific bounded input is solved in the siso single input single output discrete time case it is shown that in most situations the optimal solution will not exist but given any epsilon 0 it is possible to find a suboptimal solution with performance within epsilon of the optimal performance the proposed approach is extended to the problem of shaping the error transient response it is shown how time domain templates can be used in this problem in the same way that frequency weighting functions are used in the h sup infinity and h sup 2 problems

tensor fields on crystals a new method is presented to determine the irreducible representations of the space group of a crystal contained in the representation whose basis functions are the components of a tensor field defined on the atoms of a crystal this reducible representation is the direct product of a tensor representation dependent only on the tensor and a permutation representation dependent only on how the atoms permute under elements of the space group the permutation representation is first separately reduced prior to the reduction of the direct product the permutation representation is shown to be an induced representation and its reduction is facilitated using the theory of induced representations examples and tables of results of applying this method are given in the case of a polar vector tensor field applicable to lattice vibrational problems and crystals as the diamond structure of space group symmetry 07h

on overshoot and nonminimum phase zeros it is widely known that real nonminimum phase zeros lead to step response undershoot and that the size of the undershoot necessarily tends to infinity as the settling time tends to zero in this note we show that the presence of two or more real nonminimum phase zeros can lead to step response overshoot in addition to undershoot a lower bound on the overshoot is derived and it is shown that the overshoot like the undershoot necessarily tends to infinity as the settling time tends to zero the results are derived for single input single output linear time invariant continuous time systems and apply to both open loop control and general two degree of freedom closed loop control

symmetry properties of direct sum systems an interpretation of double coset decompositions of groups is given in terms of the construction of systems from similar disjoint subsystems a natural labelling scheme is developed for the direct product states of systems of this type providing an extension of the concept of unique labelling an application of the decoupling transformation to finite direct sum systems is investigated

a new control method for state constrained nonlinear switched systems with application to chemical process this paper presents a new control method for a class of nonlinear switched systems in strict feedback form with a state constraint in the proposed approach a nonlinear mapping is first introduced to transform the problem of controlling the switched system with state constraint to a new problem of regulating the transformed system without a constraint by using the backstepping technique the designed state feedback controller ensures that the corresponding closed loop system is asymptotically stable without violation of the constraint and that all closed loop signals keep bounded furthermore we explore the use of a coordinate transformation to deal with an asymmetric state constraint as a generalised approach in the end an application example on a chemical process is shown to demonstrate the efficacy of the obtained results

boundary control design for extensible marine risers in three dimensional space abstract a design of boundary controllers is proposed for practical exponential stabilization of extensible marine risers in three dimensional 3d space under sea loads the design removes flaws in existing works two lyapunov type theorems are developed for study of existence and uniqueness and stability of nonlinear evolution systems in hilbert space these theorems have their potential use in control design and stability analysis for flexible systems including marine risers

almost sure exponential stability of dynamical systems driven by levy processes and its application to control design for magnetic bearings abstracta lyapunov type theorem is developed to study well posedness and almost surely k exponential stability of dynamical systems driven by levy processes sufficient conditions imposed by the t

control of nonlinear systems with output tracking error constraints and its application to magnetic bearings a constructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficiently smooth reference trajectory asymptotically under a suitable condition on the initial output tracking error the proposed controllers guarantee the output tracking error within a symmetric or an asymmetric pre specified limit range and boundedness of all signals of the closed loop system a transformation is introduced to take care of the output tracking error constraint smooth and or p times differentiable step functions are proposed and incorporated in the output tracking error transformation to overcome difficulties due to the asymmetric limit range on the output tracking error as a result there are no switchings in the proposed controllers despite the asymmetric limit range the proposed control design is then applied to design a tracking controller for active magnetic bearings as an illustrating application

controller synthesis for sign invariant impulse response in this paper we consider the problem of designing controllers for discrete time linear time invariant lti plants that render the closed loop impulse response nonnegative such systems have a non undershooting and non overshooting step response we first show that the impulse response of any discrete time lti system changes sign at least r times if it has r real positive zeros outside a circular disk centered at the origin and containing all its poles we then show that a necessary and sufficient condition on the plant for the existence of a compensator that makes the closed loop impulse response sign invariant is that there be no real positive nonminimum phase plant zeros finally we show by construction how such a compensator may be synthesized when the plant does satisfy the existence condition

conditions that guarantee no overshoot for linear systems in practical control problems it is often desirable to make setpoint changes without overshoot in this paper necessary and sufficient conditions are presented which guarantee that linear state space models will not exhibit overshoot several examples illustrate the utility and simplicity of the new results

optimal pole placement design for siso discrete time systems in this paper we incorporate the placement of one real closed loop pole into a compensator design framework based upon the youla parameterization duality theory and linear programming this framework has been used to design discrete time compensators to solve the l sub 1 controller design problem as well as other related time domain optimization problems previous work on these problems has focused on deadbeat systems it is known that these can require high order controllers part of the motivation for this work is to improve the tradeoff between controller order and performance over that using deadbeat control

barrier lyapunov functions for the control of output constrained nonlinear systems in this paper we present control designs for single input single output siso nonlinear systems in strict feedback form with an output constraint to prevent constraint violation we employ a barrier lyapunov function which grows to infinity when its arguments approach some limits by ensuring boundedness of the barrier lyapunov function in the closed loop we ensure that those limits are not transgressed besides the nominal case where full knowledge of the plant is available we also tackle scenarios wherein parametric uncertainties are present asymptotic tracking is achieved without violation of the constraint and all closed loop signals remain bounded under a mild condition on the initial output furthermore we explore the use of an asymmetric barrier lyapunov function as a generalized approach that relaxes the requirements on the initial conditions we also compare our control with one that is based on a quadratic lyapunov function and we show that our control requires less restrictive initial conditions a numerical example is provided to illustrate the performance of the proposed control

on undershoot in siso systems in this technical note we show that the step response of an asymptotically stable strictly proper nonminimum phase continuous time system with m1 real open right half plane zeros no conjugate complex zeros and poles and with real open left half plane zeros and poles satisfying a given bracketing condition exhibits undershoot exactly int m1 1 2 times both qualitative and quantitative arguments are also introduced to highlight the main issues under discussion simple examples are given to illustrate and complement the main result of this note

transient response control via characteristic ratio assignment this note develops an approach to directly control the transient response of linear time invariant control systems we begin by considering all pole transfer functions of order n for which we introduce a set of parameters spl alpha sub i i 1 n called the characteristic ratios we also introduce a generalized time constant spl tau we prove that spl alpha sub 1 and spl tau can be used to characterize the system overshoot to a step input and the speed of response respectively by independently adjusting spl alpha sub 1 and spl tau in all pole systems arbitrarily small or no overshoot as well as arbitrarily fast speed of response can be achieved these formulas are used to develop a procedure to design feedback controllers with feedforward or two parameter output feedback type for achieving time response specifications for a minimum phase plant we show that arbitrary transient response specifications namely one with independently specified overshoot and specified rise time or speed of response can be exactly attained

maximizing regions of attraction via backstepping and clfs with singularities when a nonlinear control law contains a singularity that is becomes unbounded on a set of points in the state space the region of attraction is often only a subset of the region of feasibility of this control law a method which is well known to suffer from this difficulty is feedback linearization we show that the backstepping design in its standard form has an inherent ability to make the regions of feasibility and attraction coincide thus maximizing the latter the key observation that this paper provides is that a standard backstepping style control lyapunov function which grows unbounded on the set where the control law becomes unbounded has level sets that always remain in the feasibility region which makes the feasibility region positively invariant a simulation comparison with a feedback linearization design shows a dramatic improvement of the region of attraction with backstepping since our theorem imposes a strong assumption that the feasibility region for the first subsystem in the backstepping problem is positively invariant we present examples ranging from simple to fairly difficult which demonstrate how this condition can be satisfied

unique labelling schemes for local modes in lattices two procedures are described which together specify a unique point group labelling scheme for the irreducible components of local distortions in crystals in the first procedure the group operators are factorised into a permutation part and a local atomic point group operation the second depends on dividing the complete shells of atoms into subshells which are invariant under subgroups of the site permutation group

minimum overshoot design for siso discrete time systems the problem of designing a controller to minimize the maximum negative error due to a specific bounded input is studied it is found that the solution can be obtained by solving an infinite linear programming problem in the special case of a step input a simple analytical formula for minimum overshoot is derived for a plant with one unstable pole and one nonminimum phase zero the solution technique has potential application to other control problems which seek to minimize quantities not directly representable as a norm

analytic expressions of transfer function responses and choice of numerator coefficients zeros general analytic expressions of transfer function responses are derived in this paper the analytic forms include the numerator coefficients of the transfer function a vandermonde like matrix and a vector containing the transfer function eigenresponses the latter two only depending on the eigenvalues several characteristics of basic transient responses are derived e g their exact number of zeros an upper bound on the number of extrema of the step response is obtained an algorithm is suggested for the selection of the numerator coefficients assuming fixed eigenvalues using the derived characteristics of the basic transient responses effectively leading to a suboptimal choice furthermore the analytic formulas are used to calculate the numerator coefficients optimally by minimizing the step transient the ramp transient the parabolic transient etc simulations are presented indicating the properties of the basic transient responses and the transfer function response properties based on optimal and suboptimal choices of the numerator coefficients

zero crossings overshoot and initial undershoot in the step and impulse responses of linear systems we consider functions in the time and the frequency domain and show how the occurrence of real zeros in the frequency domain is related to the number of zero crossings overshoot and initial undershoot in the time domain this leads to simple proofs of known facts for linear time invariant systems and their generalizations in various directions in particular we consider time delay systems and differential systems of fractional order

adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults abstract in this work we present a novel control algorithm for a class of stochastic nonlinear systems with constraint requirement on the system output tracking error the gain functions are not totally known and the systems are subject to actuator faults a novel structure of barrier lyapunov function is proposed to deal with the constraint requirement in stochastic systems we show that under the proposed control scheme convergence of the system output tracking error into a small set around zero is guaranteed in the sense of mean quartic value the constraint requirement on the system output tracking error will not be violated during operation in the sense of probability the proposed scheme is also a unified approach which can handle both deterministic and stochastic nonlinear systems of a particular structure and can also handle nonlinear systems with or without system output constraint requirements an illustrative example with both deterministic and stochastic nonlinear systems is presented to further demonstrate the effectiveness of the proposed control scheme

rationality of p group actions abstract let p be a prime number g a p group of order p 4 k a field with char k p if the exponent of g is p e and k contains a primitive p e th root of unity then k v g is rational purely transcendental over k where g gl v is any linear representation of g over k

combinatorial enumeration and group representations it is shown that in addition to the number of distinct equivalence classes the representation characters of a labelling can also be derived using standard combinatorial methods these characters provide additional information on the structure of the equivalence classes which is relevant in physical applications

undershooting phenomenon and its control in linear multivariable servomechanisms this paper investigates an undershooting phenomenon which occurs in multivariable feedback control systems and a control method which suppresses the undershooting phenomenon of a type 1 1 1 servosystem is proposed since the linear optimal control loc is not concerned with detailed specifications of the response such studies should be useful for the design of real control systems

stable rationality of certain invariant fields abstract let f be a field for a finite group g let f g be the purely transcendental extension of f with transcendency basis x g g g let f g g denote the fixed field of f g under the action of g let w be a primitive p 1 st root of 1 and let i be the ideal p w a in z w where a is a primitive p 1 st root of 1mod p we show that if g be the semi direct product of a cyclic group of order p by a cyclic group of order prime to p if i is principal and if f contains a primitive g th root of 1 then f g g is stably rational over f it is not known whether the set of primes p for which i is principal is finite or infinite we also show that if p is an odd prime and g is a non abelian group of order p 3 then f g g is stably rational over f provided that f contains a primitive g th root of 1

nonovershooting and monotone nondecreasing step responses of a third order siso linear system this paper presents the necessary and sufficient conditions for a third order single input single output siso linear system to have a nonovershooting or monotone nondecreasing step response if the transfer function of an overall system has real poles a necessary and sufficient condition is found for the nonovershooting or monotone nondecreasing step response in the case of complex poles one sufficient condition and two necessary conditions are obtained the resulting conditions are all in terms of the coefficients of the numerator of the transfer function simple calculations can be used to check a system for the nonovershooting or monotone nondecreasing step response another feature is that the conditions in terms of pole zero configurations can be easily derived from the present results

branching processes in the annni model the mean field equations of the simple cubic annni model are studied on finite lattices the results are consistent with the sequence of distinct commensurate phases 2k 13 k 1 2 3 springing from the multiphase point found using low temperature series expansions moreover evidence for new structure combination branching processes is presented which generate phases of type 2l3 m 2l 13 n or 23l m 23l 1 n where l m and n are integers

on undershoot in scalar discrete time systems we identify a class of asymptotically stable strictly proper non minimum phase scalar discrete time systems whose step response is shown to exhibit undershoot a given number of times the conditions governing this correspondence can be verified by inspection and have a simple expression in terms of the zero pole locations of the underlying system both qualitative and quantitative aspects of the undershooting phenomenon are discussed and a simple but non trivial example is used to gain further insight into the main result of this paper

fundamental limitations on the time domain shaping of response to a fixed input in this paper we examine time domain limitation of performance problems in feedback control system design the main result is a theorem which gives a dual formulation to the problem of determining absolute limits on the time domain shaping of the response to a fixed input the duals that arise are particularly illuminating they have a simple interpretation as optimizing the impulse response of a transfer function whose poles are readily constructed from the data much insight is obtainable from the dual for example in helping to classify classes of plants with the same quantitative behavior new results on classical performance measures such as overshoot and undershoot are presented we also examine minimization of the difference between the maximum and minimum values of the error response a quantity we term fluctuation

finite time stabilisation of a class of switched nonlinear systems with state constraints abstractthis paper investigates the finite time stabilisation for a class of switched nonlinear systems with state constraints some power orders of the system are allowed to be ratios of positive even integers over odd integers a barrier lyapunov function is introduced to guarantee that the state constraint is not violated at any time using the convex combination method and a recursive design approach a state dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed loop system is finite time stable without violation of the state constraint two examples are provided to show the effectiveness of the proposed method

sign weighted peak minimization problem for feedback systems this note studies the problem of minimizing a parameterized convex combination of the overshoot and undershoot of a single input single output siso discrete time system to a fixed input we provide a simple condition for the solution existence and characterize the structure of optimal solutions it is shown that a known l sub spl infin suboptimal scheme also works in our problem in addition we make a comparative analysis with the l sub spl infin problem

induction theorems on the stable rationality of the center of the ring of generic matrices following procesi and formanek the center of the division ring of rn x n generic matrices over the complex numbers c is stably equivalent to the fixed field under the action of sn of the function field of the group algebra of a zsn lattice denoted by gn we study the question of the stable rationality of the center cn over the complex numbers when rn is a prime in this module theoretic setting let n be the normalizer of an rn sylow subgroup of sn let m be a zsn lattice we show that under certain conditions on m inductionrestriction from n to sn does not affect the stable type of the corresponding field in particular c gn and c zg0zn gn are stably isomorphic and the isomorphism preserves the sn action we further reduce the problem to the study of the localization of gn at the prime n all other primes behave well we also present new simple proofs for the stable rationality of cn over c in the cases r 5 and rn 7

influence of zero locations on the number of step response extrema abstract a new bounding theorem for the number of extrema that may occur in the step response of a stable linear system is presented the derivation of an easily computed upper bound is given to complement literature results which have previously established the existence of a lower bound the theorem requires knowledge of the pole zero configuration of the transfer function and is applicable to stable systems with real zeros and real poles

control of reverse reaction processes via a pseudo predictor a scheme for feedback control of reverse reaction processes characterised by stable non minimum phase transfer functions is described the approach is based on a pseudo predictor which is essentially a pade approximation to a smith predictor an example demonstrates a trade off involved and shows the decisive contribution to tightness of control made by the pseudo predictor

control system design via infinite linear programming in this paper we deal with the problem of designing non overshooting feedback control systems when the input is a step we also consider the more general problem of designing controllers to track a step optimally with some predetermined amount of allowable overshoot these problems are cast as infinite linear programming problems we show that both these problems always have a solution under some standard assumptions it is then shown that the counterpart of this problem that is the problem of designing non undershooting feedback control systems need not have a solution in general but it is proved that one can always design a feedback controller to achieve as little percentage undershoot as desired finally it is shown that the problem of designing controllers to simultaneously satisfy bounds on the overshoot and undershoot always has a solution if some undershoot is allowed for the duals to the infinite linear programming problems are formulated and the absense of a duality gap is established fo

linear matrix inequalities for globally monotonic tracking control this paper addresses the problem of achieving monotonic tracking control for any initial condition also referred to as global monotonic tracking control this property is shown to be equivalent to global non overshooting as well as to global non undershooting i e non overshooting and non undershooting for any initial condition respectively the main objective of this paper is to prove that a stable system is globally monotonic if and only if all the rows of the output matrix are left eigenvectors of the space transition matrix this property allows one to formulate the design of a controller which ensures global monotonic tracking as a convex optimization problem described by a set of linear matrix inequalities lmis

the unique labelling of states via mackey s theorem a new approach to finding unique labels for many electron states in multicentre systems is described and a particular example eight electrons in s states on eight centres is worked out in detail this approach is shown to provide a labelling with a more direct physical interpretation than has previously been found

unique labelling of many electron states in multicentre systems general methods of generating complete sets of states for l or 2n electrons in s states on n centres are described it is shown that a unique labelling of these states can always be obtained using a fictitious sn symmetry of the n centres explicit descriptions of eight seven and four electrons on eight centres are derived and the problem of determining a unique labelling for these states on rigid eight centre structures with cubic and lower symmetry is solved

control of nonlinear systems with partial state constraints using a barrier lyapunov function this article addresses the problem of control design for strict feedback systems with constraints on the states to prevent the states from violating the constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approaches some finite limits based on blf based backstepping we show that asymptotic output tracking is achieved without violation of any constraint provided that the initial states and control parameters are feasible we also establish sufficient conditions to ensure feasibility which can be checked offline without precise knowledge of the initial states the feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem in the presence of parametric uncertainties blf based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation to relax the feasibility conditions asymme

controller design with multiple objectives in this paper we study multi objective control problems that give rise to equivalent convex optimization problems we develop a uniform treatment of such problems by showing their equivalence to linear programming problems with equality constraints and an appropriate positive cone we present some specialized results on duality theory and we apply them to the study of three multi objective control problems the optimal l sub 1 control with time domain constraints on the response to some fixed input the mixed h sub 2 l sub 1 control problem and the l sub 1 control with magnitude constraint on the frequency response what makes these problems complicated is that they are often equivalent to infinite dimensional optimization problems the characterization of the duality relationship between the primal and dual problem allows us to derive several results these results establish connections with special convex problems linear programming or linear matrix inequality problems uncover finite dimensional structures in the optimal solution when possible and provide finite dimensional approximations to any degree of accuracy when the problem does not appear to have a finite dimensional structure to illustrate the theory and highlight its potential several numerical examples are presented

a technique for choosing zero locations for minimal overshoot an approach is presented to the specification of optimal overshoot controllers when the controller order is fixed and the closed loop system poles are at a fixed location the essential effect of the technique is to pick the best possible locations of the free zeros of the system in terms of minimizing the overshoot the solution is obtained by solving an affine minimax optimization problem an example illustrates how this technique can be used as a design aid when it is necessary to trade off conflicting design requirements such as overshoot and settling time specifications it is shown that the method is not restricted to the deadbeat case but can also be used for any prescribed set of closed loop poles

block backstepping control of mimo systems based on the lyapunov stability theorem a methodology of designing the block backstepping controller for a class of multi input multi output mimo systems is proposed to solve the tracking problem some adaptive mechanisms are embedded both in the virtual input controller and in the backstepping controllers so that not only are the perturbations suppressed but also some knowledge of the upper bound of perturbations is not required finally an example of controlling a two axis piezoelectric microposition is used to demonstrate the feasibility of the proposed methodology

synthesis of linear multivariable regulators this paper generalizes the results obtained by the authors in 1 and presents new results on the construction of proper controllers for linear multivariable regulators these results may lead to efficient computation methods that do not involve smith forms or the order relations used in 1 to construct proper controllers the methods are based on the recently developed theory of generalized polynomials 2 we discuss several numerical algorithms and how they can be applied to the regulator problem we also point out an important computational problem in need of an efficient numerical algorithm

classification of configurations of systems of identical particles on finite sets all possible configurations of a system of n identical particles are classified for the case when the configuration space q of a single particle reduces to a finite set the classification is achieved by means of a combinatorial analogue of the duality of weyl two groups the pauli group permuting identical particles and the symmetric group on q act on the nth cartesian power of q these actions mutually commute and their orbit structure is classified by appropriate epikernels moreover each stratum of each group is invariant under the dual action which yields a coarsening of permutation representations acting on appropriate sets of orbits it is shown that such a coarsening recovers the geometric symmetry for the case when particles are indistinguishable

lattices over cyclic groups and noether settings abstract for each positive integer m let m be a primitive mth root of 1 given a prime p let a be an integer which is a primitive root of 1 mod p let i p m be the ideal in z m generated by p and m a let g be a cyclic group of order n such that the flasque class of any maximal projective ideal in z g contains a maximal ideal u of index p for some prime p such that n divides p 1 and such that i p n is principal it is not known whether the number of groups satisfying this property is finite or infinite we show that if f is a field of characteristic zero containing all nth roots of 1 then for any z g lattice m the fixed subfield of f m is stably rational over f if f also contains primitive mth roots of 1 for all natural numbers m then for any finite g module t the fixed subfield of the noether setting of the group g t g is stably rational over f

classification and determination of irreducible bases for induced representations for chains of subgroups of finite groups the problem of classification and determination of standard irreducible bases for induced representations of an arbitrary finite group is discussed a general prescription for classification and determination of these bases for an arbitrary induced representation is proposed and an extra independent prescription for the special case of primitive representations is given relations between appropriate transformation coefficients are investigated and in particular a matrix similar to the racah recoupling matrix from theory of multiple coupling of angular momentum is introduced

nonovershooting control of strict feedback nonlinear systems a means of obtaining a nonovershooting output tracking response for single input single output siso strict feedback nonlinear systems is introduced with the proposed method arbitrary reference trajectories can be tracked from below for arbitrary initial conditions as long as the initial value of the plant output is strictly below the initial value of the reference trajectory in addition a design is presented for approximately nonovershooting control in the presence of disturbances where the amount of overshoot can be made arbitrarily small by appropriately choosing the control gains finally an output feedback example shows the ability of our approach to ensure arbitrarily small overshoot where the overshoot is caused by the initial condition of the unmeasured part of the state

structure and representations of the symmetry group of the four dimensional cube in this paper we give explicitly the description of the structure the characters and the complete system of irreducible representations of the hyperoctahedral group in four dimensions which we call w4 from the german wurfel in a second step we do the same for the subgroup sw4 which is formed by all pure rotations contained in w4

bounded controllers for formation stabilization of mobile agents with limited sensing ranges a constructive method is presented to design bounded cooperative controllers that force a group of n mobile agents with limited sensing ranges to stabilize at a desired location and guarantee no collisions between the agents the control development is based on new general potential functions which attain the minimum value when the desired formation is achieved and are equal to infinity when a collision occurs a p times differential bump function is introduced and embedded into the potential functions to deal with the agent limited sensing ranges an alternative to barbalat s lemma is developed to analyze stability of the closed loop system extension to formation tracking is also addressed

symmetry coordinates for oh atomic shells the group factorisation and correlation theorem methods used previously to provide a unique labelling of atomic shell symmetry coordinates are shown to give also a simple means for deriving explicit expressions for these coordinates results are given for the 12 atom shell and the two types of 24 atom shells in oh symmetry

brief paper control of nonlinear systems with time varying output constraints this paper presents control design for strict feedback nonlinear systems with time varying output constraints an asymmetric time varying barrier lyapunov function blf is employed to ensure constraint satisfaction by allowing the barriers to vary with the desired trajectory in time the initial condition requirements are relaxed through a change of tracking error coordinates we eliminate the explicit dependence of the blf on time thereby simplifying the analysis of constraint satisfaction we show that asymptotic output tracking is achieved without violation of the output constraint and also quantify the transient performance bound as a function of time that converges to zero to handle parametric model uncertainty we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation the performance of the proposed control is illustrated through a simulation example

unique labelling of symmetry coordinates and cyclic regions in crystals earlier work on unique labelling schemes in oh symmetry is extended to include 48 atom shells and the symmetry coordinates of shells subject to periodicity conditions a new approach to labelling is introduced based on the concept of cyclic regions in a crystal these are described by finite factor groups of the crystallographic space group which contain the isogonal group as a subgroup some examples are worked out in detail

technical communique on type number concept in fractional order systems in this note the type number concept is defined for fractional order systems based on this definition it is shown that fractional order systems having type numbers more than 1 can not track some classes of reference inputs without any overshoot

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

non overshooting output tracking of feedback linearisable nonlinear systems the problem of non overshooting output tracking of feedback linearisable single input single output nonlinear systems is considered we present a controller design procedure which makes use of feedback linearisation and global coordinate transformation techniques and is applicable to the cases with a variety of reference inputs and possibly non zero initial conditions for systems with low relative order the sets of feasible controller parameters are constructed and the presented conditions for determining these sets are sufficient and necessary for systems with higher relative order an approach to construct such sets is proposed where the conditions are sufficient two illustrative examples are provided to show the effectiveness of the results

robust distributed model predictive control of linear systems with structured time varying uncertainties abstractin this work synthesis of robust distributed model predictive control mpc is presented for a class of linear systems subject to structured time varying uncertainties by decomposing a global system into smaller dimensional subsystems a set of distributed mpc controllers instead of a centralised controller are designed to ensure the robust stability of the closed loop system with respect to model uncertainties distributed state feedback laws are obtained by solving a min max optimisation problem the design of robust distributed mpc is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints an iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance the simulation results show the effectiveness of the proposed robust distributed mpc algorithm

constrained control of input output linearizable systems using control sharing barrier functions abstract control barrier functions cbfs have been used as an effective tool for designing a family of controls that ensures the forward invariance of a set when multiple cbfs are present it is important that the set of controls satisfying all the barrier conditions is non empty in this paper we investigate such a control sharing property for multiple cbfs and provide sufficient and necessary conditions for the property to hold based on that we study the tracking control design problem of an input output linearizable system with multiple time varying output constraints where the output constraints are encoded as cbfs and the barrier conditions are expressed as hard constraints in a quadratic program qp whose feasibility is guaranteed by the control sharing property of the cbfs with the controller generated from the qp the output constraints are always satisfied and the tracking objective is achieved when it is not conflicting with the constraints the effectiveness of our control design method is illustrated by two examples