2d residual generation and dead beat observers abstract in this paper we consider the 2d residual generation problem in an algebraic context an algorithmic method that provides a complete family of residual generators is presented and some connections between 2d residual generation and 2d dead beat observer synthesis are investigated

number and length of attractors in a critical kauffman model with connectivity one the kauffman model describes a system of randomly connected nodes with dynamics based on boolean update functions though it is a simple model it exhibits very complex behavior for critical parameter values at the boundary between a frozen and a disordered phase and is therefore used for studies of real network problems we prove here that the mean number and mean length of attractors in critical random boolean networks with connectivity one both increase faster than any power law with network size we derive these results by generating the networks through a growth process and by calculating lower bounds

matrix rank based conditions for reachability controllability of discrete linear repetitive processes abstract this paper uses both 2d and standard or 1d representations of the dynamics of discrete linear repetitive processes to characterise their reachability controllability properties the major new results are a 1d representation of constant dimensions and characterisations of reachability controllability in terms of matrix rank based conditions

robust mixed generalized h sub 2 h sub spl infin filtering of 2 d nonlinear fractional transformation systems this study considers robust filtering problems for uncertain two dimensional 2 d discrete systems in nonlinear fractional transformation nft representations like one dimensional 1 d systems the nft in this paper serves to complement the linear fractional transformation lft linear matrix inequality lmi formulations are given to analyze as well as synthesize robust filters numerical examples show the advantage of the nft over the lft in terms of not only computational savings but also substantial performance gains and verify the efficiency of the proposed techniques

state analysis of boolean control networks with impulsive and uncertain disturbances in this paper we put forward a method for the state analysis of boolean control networks with impulsive and uncertain disturbances in detail we introduce the probability in the analysis of the state of boolean networks mathematically the stp as the analytical tool has be used for the modeling of uncertainty in addition we give a mathematical proof for the model lastly we conduct some simulations which validate the efficiency for this model

controllability analysis of two dimensional systems using 1d approaches working with the 1d form of 2d systems is an alternative strategy to reduce the inherent complexity of 2d systems to achieve the 1d form of 2d systems different from the so called wam model a new row column process was proposed recently the controllability analysis of this new 1d form is explored in this note two new notions of controllability named wam controllability and directional controllability for the underlying 2d systems are defined corresponding conditions on the wam controllability and directional controllability are derived which are particularly useful for the control problems of 2d systems via 1d framework according to the presented directional controllability a directional minimum energy control input is derived for 2d systems a numerical example demonstrates the applicability of the presented analysis

the existence and design of functional observers for two dimensional systems abstract this paper is concerned with functional observers for two dimensional 2d systems described by the fornasini marchesini local state space second model a necessary and sufficient condition is given for the existence of asymptotic functional observers a more tractable necessary condition for the existence of asymptotic functional observers is also presented as it helps exclude those 2d systems for which there is no asymptotic functional observer a constructive design method is then proposed for the design of asymptotic functional observers using a rank condition on the given system matrices and a linear matrix inequality lmi technique two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method

optimal control of two dimensional systems necessary and sufficient conditions for the existence and the uniqueness of the solution of the optimal control problem of discrete time linear time invariant two dimensional systems are determined given a system that satisfies these conditions the optimal control law is obtained using an algebraic riccati equation with coefficients in the polynomial ring r z since the feedback implementation of this law does not preserve the causal structure of the system suboptimal control laws are also discussed that lead to a weakly causal two dimensional system finally some important connections between optimal control in an mathfrak l 2 setting and mathfrak l infty stabilization are investigated

on the structure of 2 d observers this note gives necessary and sufficient conditions for asymptotic reconstructibility of the state of multivariable 2d systems the existence and the structure of the observers are related to the matrices appearing in a bezout identity a counterexample shows that the state estimation cannot be performed in general by a static feedback on the estimation error this note includes also a technique for designing dynamic state observers

unknown input observers for 2d state space models in this paper dead beat unknown input observers uios for two dimensional 2d state space models are investigated dead beat uios are observers which produce an exact estimate of the original system state trajectory after a finite number of evolution steps independently of the system and observer initial conditions and of the unknown disturbances that affect the system functioning necessary and sufficient conditions for the existence of dead beat uios are provided as well as a parameterization of all dead beat uio transfer matrices comparisons with luenberger type uios are also carried out and the extension of the paper results to the case of asymptotic uios with a given rate of convergence and to roesser models are finally discussed

state feedback stabilization for boolean control networks state feedback stabilization for boolean control networks is investigated in this technical note based on the algebraic representation of logical dynamics in terms of the semi tensor product of matrices a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a general control design approach is proposed when global stabilization is feasible via state feedback instead of designing the logical form of a stabilizing feedback law directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form an example is worked out to illustrate the proposed design procedure

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

a minimum time control for boolean control networks with impulsive disturbances this paper investigates a mayer type optimal control and minimum time control of a boolean control network bcn with impulsive disturbances using the semi tensor product the bcn with impulsive disturbances is converted into algebraic discrete time impulsive dynamic systems and several necessary conditions for optimality are derived then we consider the problem of steering a bcn with impulsive disturbances from a given initial state to a desired state in minimal time and a necessary condition stated in the form of maximum principle is obtained for a control to be time optimal it shows that the impulsive disturbances play an important role in the optimal control problem for bcns at last a biological example is given to illustrate the effectiveness and advantage of the obtained results

fitting the student t distribution to grouped data with application to a particle scattering experiment experimental data are presented for which the student t distribution provides a plausible model a grouped maximum likelihood estimation approach is developed a data set is presented that is accurately modeled by a distribution with tails heavier than a cauchy distribution

the general state space model for a two dimensional linear digital system the general state space model for a 2 d linear digital system is presented a new definition of state transition matrix is given based on the definition it is easy to calculate the state transition matrix for any linear digital system the general response formula for a system follows simply from the definition a new definition of the characteristic function of a system and a theorem parallel to the cayley hamilton theorem are also given the presented results apply to any linear causal system

h sub spl infin filtering of 2 d discrete systems this paper deals with h sub spl infin filtering of two dimensional 2 d linear discrete systems described by a 2 d local state space lss fornasini marchesini 1978 second model several versions of the bounded real lemma of the 2 d discrete systems are established the 2 d bounded real lemma allows us to solve the finite horizon and infinite horizon h sub spl infin filtering problems using a riccati difference equation or a riccati inequality approach further a solution to the infinite horizon h sub spl infin filtering problem based on a linear matrix inequality lmi approach is developed our results extend existing work for one dimensional 1 d systems to the 2 d case and give a state space solution to the bounded realness of 2 d discrete systems as well as 2 d h sub spl infin filtering for the first time numerical examples are given to demonstrate the riccati difference equation approach to the 2 d finite horizon h sub spl infin filtering problem and the lmi approach to the 2 d infinite horizon h sub spl infin filtering problem

common eigenvector approach to exact order reduction for roesser state space models of multidimensional systems abstract the well known popov belevitch hautus pbh tests play an important role in the kalman decomposition of 1 d systems and reveal the relationship among the eigenvalues the eigenvectors and the reducibility of a given 1 d state space model this paper is to try to generalize the pbh tests to the n d case for the exact reducibility of n d roesser models by exploiting the so called common eigenvectors specifically the notion of constrained common eigenvectors is introduced for the first time which provides insight into the relationship between reducibility and multiple eigenvalues based on this result new reducibility conditions and the corresponding reduction procedure are developed for n d roesser models it will be shown that this common eigenvector approach is applicable to a larger class of roesser models for which the existing approaches may not be applied to do further order reduction a grobner basis approach is proposed to compute such a constrained common eigenvector which also leads to an equivalent reducibility condition moreover a generalization to the state delay case is also given so that the eigenvalues of both the system matrix and the state delay system matrix can be treated simultaneously

bifurcation analysis of a mathematical model for genetic regulatory network with time delays in this paper we aim to investigate the dynamics of a gene regulatory network which is a time delayed version of the model proposed by elowitz and leibler nature 403 2000 335 338 based on the normal form theory and center manifold reduction hopf bifurcations including the bifurcation direction and stability of the bifurcated periodic orbits are investigated we also discuss effects of transcriptional rate and time delay on the amplitude and period of the oscillation of the network it shows that variations of time delay or transcriptional rate can change the period and amplitude of the oscillation more precisely i the amplitude increases with small time delay while the change of amplitude is not sensitive to relatively large time delay however the robustness of amplitudes is not true any more for the case of using the transcriptional rate as parameter where amplitude always increases quickly and linearly with the transcriptional rate ii the period of oscillation increases as the time delay increases but it grows up initially as the transcriptional rate increases and then keeps unchanged to certain constant value which implies that the robustness of period to the transcriptional rate variations occurs our numerical simulations also support the theoretical conclusions namely both suggest that time delay and transcriptional rate can be used as control parameters in genetic regulatory networks

on robust control invariance of boolean control networks this paper investigates the robust control invariance of boolean control networks bcns via the semi tensor product of matrices firstly based on an algebraic state space representation of bcns two necessary and sufficient conditions are presented to check whether or not a given set is a robust control invariant set under a given state feedback controller secondly by defining a series of suitable sets all possible state feedback gain matrices under which a given set is a robust control invariant set are characterized an illustrative example is presented to demonstrate the obtained new results

analysis and control of the jump modes behavior of 2 d singular systems part ii regular observer and compensator design this paper considers the problems of regular observer and compensator design for 2 d acceptable singular systems first the notions of jump mode reconstructability and jump mode reachability for 2 d acceptable singular systems are proposed necessary and sufficient conditions are presented for the jump mode reconstructability and reachability respectively then we show that there exists a reduced order regular observer for a 2 d acceptable singular system if the system is detectable and jump mode reconstructable while there exists a reduced order regular compensator for a 2 d acceptable singular system if the system is stabilizable and jump mode reachable

controllability and reconstructibility conditions for 2 d systems necessary and sufficient multi input multioutput conditions for local controllability and causal reconstructibility of 2 d systems are presented which are based on 2 d matrix polynomial equations the conditions are computationally attractive only unimodular operations in a euclidean ring are required in addition when testing controllability and or reconstructibility one obtains a deadbeat regulator and or an exact observer as by products

further observations concerning the strict system equivalence of polynomial system matrices over r s z abstract previous studies concerning the strict equivalence of polynomial system matrices over s z are continued with particular reference to conditions under which particular forms of such system matrices are strictly system equivalent to an appropriate canonical form

stability and stabilization of boolean networks with impulsive effects abstract this paper investigates the stability and stabilization of boolean networks with impulsive effects after giving a survey on semi tensor product of matrices we convert a boolean network with impulsive effects into impulsive discrete time dynamics then some necessary and sufficient conditions are given for the stability and stabilization of boolean networks with impulsive effects finally examples are provided to illustrate the efficiency of the obtained results

stability of nonlinear discrete repetitive processes with markovian switching repetitive processes are a class of 2d systems that operate over a subset of the upper right quadrant of the 2d plane applications include iterative learning control where experimental verification has been reported based on a linear time invariant model approximation of the dynamics this paper considers discrete nonlinear repetitive processes with markovian switching and applies as one application the resulting stability theory to iterative learning control for a class of networked systems where time varying dynamics arise

existence of maximum likelihood estimates for interval censored data from some three parameter models with a shifted origin summary given data in the form of interval censored observations from a three parameter distribution practical criteria are established for the existence of maximum likelihood estimates for three kinds of parameter space these criteria can be derived by analysing the behaviour of the log likelihood near a type of boundary of the parameter space called the probability contents inner boundary the effectiveness of the criteria is discussed in the case where the underlying distribution is a three parameter log normal distribution the efficiency of the criteria is evaluated by simulation

structural invariants of two dimensional systems in this paper some fundamental structural properties of two dimensional 2 d systems which remain invariant under feedback and output injection transformation groups are identified and investigated for the first time as is well known structural invariants that follow from the definition of controlled and conditioned invariance output nulling input containing self bounded and self hidden subspaces play pivotal roles in many theoretical studies of systems theory and in the solution of several control estimation problems these concepts are developed and studied within a 2 d context in this paper

almost disturbance decoupling with internal stability the almost disturbance decoupling problem with internal stability is solved in terms of the geometric concepts of linear systems theory the solution gives necessary and sufficient conditions for the existence of a dynamic output feedback controller such that in the closed loop system the disturbances are quenched say in the h sup infinity sense up to any degree of accuracy while maintaining a stable system matrix

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

output feedback control of discrete linear repetitive processes abstract repetitive processes are a distinct class of 2d systems i e information propagation in two independent directions of both systems theoretic and applications interest they cannot be controlled by direct extension of existing techniques from either standard termed 1d here or 2d systems theory here we give new results on the relatively open problem of the design of physically based control laws using an lmi setting these results are for the sub class of the so called discrete linear repetitive processes which arise in applications areas such as iterative learning control

cal h _ infty and cal h _ 2 norms of 2 d mixed continuous discrete time systems via rationally dependent complex lyapunov functions this paper addresses the problem of determining the cal h infty and cal h 2 norms of 2 d mixed continuous discrete time systems the first contribution is to propose a novel approach based on the use of complex lyapunov functions with even rational parametric dependence which searches for upper bounds on the sought norms via linear matrix inequalities lmis the second contribution is to show that the upper bounds provided are nonconservative by using lyapunov functions in the chosen class with sufficiently large degree the third contribution is to provide conditions for establishing the tightness of the upper bounds the fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient lmi condition for establishing positive semidefiniteness of even hermitian matrix polynomials this result is also exploited to derive an improved necessary and sufficient lmi condition for establishing exponential stability of 2 d mixed continuous discrete time systems some numerical examples illustrate the proposed approach it is worth remarking that nonconservative lmi methods for determining the cal h infty and cal h 2 norms of 2 d mixed continuous discrete time systems have not been proposed yet in the literature

global stability and stabilization of switched boolean network with impulsive effects the present paper investigates the global stability and stabilization of switched boolean network with impulsive effects by using the semi tensor product the algebraic form of the switched boolean network with impulsive effects is obtained then sufficient and necessary condition is presented for the global stability of the switched boolean network with impulsive effects furthermore sufficient and necessary conditions are provided for the stabilization of the switched boolean network with impulsive effects under two types of controls finally examples are presented to illustrate the main results

local controllability reachability and reconstructability of the general singular model of 2d systems necessary and sufficient conditions for the local controllability reachability and reconstructability of the general singular model of 2d linear systems are established

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

fault detection and isolation of two dimensional 2d systems abstract in this work we develop a novel fault detection and isolation fdi scheme for discrete time two dimensional 2d systems that are represented by the fornasini marchesini model ii fmii this is accomplished by generalizing the basic invariant subspaces including unobservable conditioned invariant and unobservability subspaces of 1d systems to 2d models these extensions have been achieved and facilitated by representing a 2d model as an infinite dimensional inf d system on a banach vector space and by particularly constructing algorithms that compute these subspaces in a finite and known number of steps by utilizing the introduced subspaces the fdi problem is formulated and necessary and sufficient conditions for its solvability are provided sufficient conditions for solvability of the fdi problem for 2d systems using both deadbeat and lmi based filters have also been developed moreover the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the currently available 2d geometric methods in the literature

stabilization controllability and optimal control of boolean networks with impulsive effects and state constraints the present note investigates the stabilization controllability and optimal control problem of boolean networks with impulsive effects and state constraints by using the semi tensor product method the algebraic form of the boolean networks with impulsive effects and state constraints is derived the stabilization and controllability issues of the systems are investigated and some necessary and sufficient conditions are obtained in addition the mayer type optimal control problem is also studied and algorithms are provided to design the control sequence furthermore examples are given to illustrate the main results

robust mixed spl hscr sub 2 spl hscr sub spl infin filtering of 2 d systems this paper deals with several challenging problems of robust filtering for two dimensional 2 d systems first of all new linear matrix inequality lmi characterizations for the spl hscr sub spl infin and spl hscr 2 norms of 2 d systems are introduced and thoroughly established based on these preparatory results convex lmi characterizations for robust spl hscr sub spl infin spl hscr sub 2 and robust mixed spl hscr sub 2 spl hscr sub spl infin filtering are derived the efficiency and viability of the proposed techniques and tools are demonstrated through a set of numerical examples

an observer design for linear time delay systems an observer design is proposed for linear systems with time delays the key to the design is to find a generalized coordinate change such that in the new coordinates all the time delay terms are injected by the system s output the existence of such a coordinate change is guaranteed by a rank condition on the observability matrix the novelty of the proposed design is clearly reflected in the multiple output case where a dimensional expansion in the coordinate change could become necessary and hence is allowed

lq optimal control for 2d roesser models of finite extent abstract this paper investigates several aspects of linear quadratic lq optimal control for roesser models over a two dimensional 2d signal index set of finite extent first we consider the characterisation and computation of open loop control laws when constraints on the system semi states are imposed at both the south west and north east boundaries of the frame i e signal index set of interest by virtue of the quarter plane causal structure of the roesser model the south west and north east boundary conditions are analogous to initial conditions and terminal constraints respectively a necessary and sufficient characterisation of optimality is obtained and explicitly computable formulae are derived to characterise the corresponding control inputs and performance index under reasonable assumptions on the problem data in the second part of the paper the problem of optimal lq control via semi state feedback is considered a 2d riccati like difference equation is introduced to characterise in a sufficient sense a solution to this problem

disturbance decoupling of boolean control networks disturbance decoupling problem ddp of boolean control networks is considered using semi tensor product of matrices and the matrix expression of logical functions a working procedure is proposed to solve the problem this procedure consists of two key design steps first how to convert a system into an output friendly coordinate frame an algorithm is provided to calculate the output friendly subspaces secondly it was shown how to find proper controllers to solve the problem if it is solvable a state variable separation form is introduced to guide the design of controllers based on the design technique necessary and sufficient conditions are obtained for the solvability of ddp

on the state reconstruction of 2d systems abstract the paper gives necessary and sufficient conditions for exact reconstrucbility of the state of 2d systems it includes also a technique for designing dynamic state observers

frequency domain lyapunov equations and performance bounds for differential linear repetitive processes repetitive processes are characterised by a series of passes through a set of dynamics defined over a finite fixed duration with explicit interaction between successive outputs in this paper a new lyapunov equation based stability condition is developed for one subclass and used to construct bounds on expected system performance

corrected maximum likelihood in non regular problems on suggere que l utilisation du produit des densites pour la fonction de vraisemblance est une mauvaise application de la methode du maximum de vraisemblance dans des cas non reguliers

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables