two degrees of freedom dead beat control system with robustness this paper deals with the design of a two degrees of freedom tdf dead beat controller with both optimal robustness and minimum settling time based on the parametrization of all stabilizing tdf controllers optimal robustness and minimum time control are achieved simultaneously the minimum time dead beat control is constructed for arbitrary real rational reference input at the same time optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability it is proved that under the same robustness criterion irrespective of its length of settling time the optimal robustness of the tdf system is always superior to that of the one degree of freedom odf system as long as its settling time is finite and they become identical only when the settling time of the odf system goes to infinity a numerical example is given to illustrate the theoretical results

coexistence states for cooperative model with diffusion abstract in this paper we are mainly concerned with a cooperative system with a saturating interaction term for one species existence of coexistence states is investigated by global bifurcation theory and exact results on regions in parameter space which have nontrivial nonnegative steady state solutions are given the stability of coexistence states is also studied

monotone methods for higher order partial difference equations abstract a nonlinear difference equation of the order n m in two independent variables nx myu x y u together with appropriate initial and periodic boundary conditions is considered several comparison results for these problems are established these results are then used to provide sufficient conditions for the convergence of monotone iterative methods numerical illustrations dwelling upon the importance of our results are also included

brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

optimal stochastic control for performance and stability robustness a design method for discrete time control systems that maintain stability with minimum performance degradation in the presence of a variety of deterministic and stochastic perturbation disturbances is presented deterministic perturbation and modeling errors are represented by maximum deviations from a nominal linear discrete time system and stochastic perturbations are modeled by generalization of the sector bound nonlinearity concept to the stochastic case based on the given bounds on deterministic and stochastic perturbations an upper bound on the quadratic performance index which is useful in assessing the performance deterioration according to the feedback gain used is found then the optimal feedback gain which minimizes this bound on the performance index is derived in the time invariant case the existence of a stabilizing property of the bound optimal controller which is obtained by minimizing an average cost per stage is shown

independent parameterization of two degree of freedom compensators in general robust tracking systems consideration is given to a general robust tracking problem in which the controlled object is a linear multivariable system having measured variables that are not necessary coincident with the output variables to be controlled a necessary and sufficient condition for the two degree of freedom compensator to achieve a robust tracking system with internal stability is given an existence condition is derived for such a compensator and the class of all such compensators is parameterized so that two specifications with respect to responses for reference commands and feedback properties can be satisfied independently by the two free parameters

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

stability and performance robustness for multivariable linear systems abstract this paper deals with both aspects of stability and performance robustness of linear systems in the time domain a linear time invariant feedback control law which yields the largest set of parameter variations is first determined it is then used as an initial guess for designing a robust control law which produces satisfactory performance for each of several operating points of the system given a priori the stability robustness properties of the resulting control law is also studied the proposed approach is applied to an example yielding larger stability bounds including satisfactory performance in comparison with recently reported results

accelerated monotone iterative methods for finite difference equations of reaction diffusion this paper is concerned with numerical methods for a finite difference system of reaction diffusion convection equation under nonlinear boundary condition various monotone iterative methods are presented and each of these methods leads to an existence comparison theorem as well as a computational algorithm for numerical solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function application is given to a model problem from chemical engineering and some numerical results including a test problem with known analytical solution are presented to illustrate the various rates of convergence of the iterations

monotone iterative methods for finite difference system of reaction diffusion equations this paper presents an existence comparison theorem and an iterative method for a nonlinear finite difference system which corresponds to a class of semilinear parabolic and elliptic boundary value problems the basic idea of the iterative method for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences from a suitable linear discrete system using upper and lower solutions as two distinct initial iterations two monotone sequences from a suitable linear system are constructed it is shown that these two sequences converge monotonically from above and below respectively to a unique solution of the nonlinear discrete equations this formulation leads to a well posed problem for the nonlinear discrete system applications are given to several models arising from physical chemical and biological systems numerical results are given to some of these models including a discussion on the rate of convergence of the monotone sequences

asymptotic behavior of solutions for a lotka volterra mutualism reaction diffusion system with time delays this paper is to investigate the asymptotic behavior of solutions for a time delayed lotka volterra n species mutualism reaction diffusion system with homogeneous neumann boundary condition it is shown under a simple condition on the reaction rates that the system has a unique bounded time dependent solution and a unique constant positive steady state solution and for any nontrivial nonnegative initial function the corresponding time dependent solution converges to the constant positive steady state solution as time tends to infinity this convergence result implies that the trivial steady state solution and all forms of semitrivial steady state solutions are unstable and moreover the system has no nonconstant positive steady state solution a condition ensuring the convergence of the time dependent solution to one of nonnegative semitrivial steady state solutions is also given

on the loop transfer recovery one method of model based compensator design for linear multivariate systems consists of state feedback design and observer design athans 1971 a key step in recent work in multivariate synthesis involves selecting an observer gain so the final loop transfer function is the same as the state feedback loop transfer function doyle and stein 1979 goodman 1984 this is called loop transfer recovery ltr this paper shows how identification of the eigenstructure of the compensators that achieve ltr makes possible a design procedure for observer gain luenberger 1971 this procedure is based on the eigenstructure assignment of the observers the sufficient condition for ltr and the stability of the closed loop system is that the plant be minimum phase the limitation of this method might arise when the plant has multiple transmission zeros

robustness of discrete time systems for unstructured stochastic perturbations several stochastic stability robustness measures are presented for nominally exponentially stable linear discrete time systems with unstructured perturbations having second moment bounds dependence of these measures on the stability degree of the nominal system and other parameters used in the procedure is illustrated by using the time evolution of the second moment of the system state and stochastic lyapunov stability results positive super martingale convergence theorems the ability of nominally exponentially stable systems to maintain stability in the presence of unstructured stochastic linear and nonlinear perturbations is demonstrated quantitative results are given to determine the maximum modeling uncertainty which can be tolerated in design upper bounds on the second moments of stochastic perturbations to maintain the mean square and almost sure stability of these systems in the presence of unstructured perturbations are obtained

design of robust state feedback laws existence criteria and computational methods are presented for finding stabilizing state feedback laws for systems with uncertain state or control matrices the uncertainties are modelled as sector bounded non linearities and feedback laws ensuring global asymptotic closed loop stability are obtained using lyapunov e direct method the algorithms essentially amount to repeatedly solving a parameter dependent riccati equation until the maximal solution becomes positive definite

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

technical communique an efficient algorithm for optimal control of pwa systems with polyhedral performance indices we present an algorithm for the computation of explicit optimal control laws for piecewise affine pwa systems with polyhedral performance indices the algorithm is based on dynamic programming dp and represents an extension of ideas initially proposed in kerrigan and mayne 2003 optimal control of constrained piecewise affine systems with bounded disturbances in proceedings of the 41st ieee conference on decision and control las vegas nevada usa december and baotic et al 2003 a new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index in proceedings of european control conference cambridge uk september specifically we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off line computations an extensive case study is provided which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature

asymptotic behavior of solutions for a cooperation diffusion model with a saturating interaction this paper is concerned with a lotka volterra cooperation diffusion model with a saturating interaction term for one species the goal of the paper is to investigate the asymptotic behavior of the time dependent solution in relation to the corresponding steady state solutions under homogeneous neumann boundary condition some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time dependent solution converges to one of the nonnegative constant steady state solutions as time tends to infinity this convergence result leads to the existence and uniqueness of a positive or nonnegative steady state solution and the global asymptotic stability of a given nonnegative constant steady state solution in terms of ecological dynamics it also gives some coexistence permanence and extinction results for the model

brief paper on a reachability problem for affine hypersurface systems on polytopes this paper studies the problem for an affine hypersurface system with n 1 inputs to reach a polytopic target set starting from inside a polytope in the state space we present a solution which begins with a characterization of solvability by open loop control and concludes with a procedure to synthesize a feedback control our emphasis is on methods of subdivision triangulation and covers which explicitly account for the capabilities of the control system in contrast with the previous literature the partition methods are guaranteed to yield a correct feedback synthesis assuming the problem is solvable by open loop control

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

parametrization of stabilizing controllers for multivariable servo systems with two degrees of freedom a necessary and sufficient condition for the existence of a servo controller is derived using the fractional representation approach for the plant whose measured variables are not necessarily coincident with its controlled outputs an independent parametrization of the servo controllers and the attainable transfer characteristics is proposed the possible classes of all controllers with integrity in the error channel or measured output channel is also clarified using the derived parametrization

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

dynamics of nonlinear parabolic systems with time delays abstract the dynamics of a coupled system of semilinear parabolic equations with discrete time delays is investigated using the method of upper and lower solutions it is shown that if the reaction function in the system possesses a mixed quasimonotone property and the corresponding elliptic system has a pair of coupled upper and lower solutions then there is a monotone iteration process which yields a pair of quasisolutions of the elliptic system and the sector between the quasisolutions is an attractor of the delayed parabolic system under some additional conditions this sector is a global attractor and the solution of the parabolic system converges to a true solution of the elliptic system the same conclusions are obtained for a coupled system of parabolic ordinary equations with time delays applications are given to three model problems arising from ecology and nuclear engineering these model problems possess multiple steady state solutions and sufficient conditions are given to ensure the stability and instability of these solutions

lqg controller synthesis with plant and noise spectral uncertainties in this paper we consider the problem of robust controller synthesis with plant and noise spectral uncertainties in lqg optimal systems we frame an algorithm for synthesizing the robust controller to minimize the least favourable cost functional j via specifying the weighting matrices q and r the wiener hopf technique in the lqg optimal system the saddle point theory and a property of the contractive operator are employed to solve this problem

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

on robust asymptotic tracking perturbations on coprime factors and parameterization of all solutions the robust asymptotic tracking problem is analyzed in this paper relative to unstructured perturbations on each coprime factor of the transfer functions from the control input to the measured and controlled outputs in each case necessary and sufficient conditions for the existence of solutions are presented which are explicitly given in terms of problem data under such conditions explicit parameterizations are given of all controllers which achieve robust asymptotic tracking in terms of free rational proper and stable matrices

feedback representation of precompensators the general case using the transfer approach we give under internal stability conditions a necessary and sufficient condition of equivalence between open loop precom pensation and a closed loop configuration that consists of dynamic output feedback and inside loop precompensation our result is the generalization of hammer s result hammer 1983 to the general case this result emphases the use of skew prime relationships the parametrization of this problem s solutions will throw new light on multipurpose controllers

two degree of freedom dead beat control system with robustness multivariable case abstract a design procedure for two degree of freedom tdf dead beat controllers for multivariable systems is presented based on the parametrization of all stabilizing tdf controllers a minimal time dead beat control system with optimal robustness is constructed for an arbitrary reference input the optimal robustness is achieved under the constraint of robust tracking a comparison of a tdf system with a one degree of freedom odf system reveals that under the same robustness criterion the optimal robustness of the tdf system is always superior to that of the odf system irrespective of its settling time it is also shown that the optimal robustness of the odf system becomes identical to that of the tdf only when the settling time of the odf system goes to infinity some numerical examples are given to illustrate the theoretical results

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

the majorant lyapunov equation a nonnegative matrix equation for robust stability and performance of large scale systems a new robust stability and performance analysis technique is developed the approach involves replacing the state covariance by its block norm matrix i e the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics a bound i e majorant for the block norm matrix is given by the majorant lyapunov equation a lyapunov type nonnegative matrix equation existence uniqueness and computational tractability of solutions to the majorant lyapunov equation are shown to be completely characterized in terms of m matrices two examples are considered for a damped simple harmonic oscillator with uncertain but constant natural frequency the majorant lyapunov equation predicts unconditional stability and for a pair of nominally uncoupled oscillators with uncertain coupling the majorant lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators a result not predictable from quadratic or vector lyapunov functions

hybrid model reference adaptive control of piecewise affine systems this paper is concerned with the derivation of a model reference adaptive control mrac scheme for multimodal piecewise affine pwa and piecewise linear systems the control allows the plant to track asymptotically the states of a multimodal piecewise affine or smooth reference model the reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability

algebraic theory of linear multivariable feedback systems this paper presents an algebraic theory for analysis and design of linear multivariable feedback systems the theory is developed in an algebraic setting sufficiently general to include as special cases continuous and discrete time systems both lumped and distributed designs are implemented by construction of a controller with two vector inputs and one vector output use of controllers of this type is shown to generate convenient stability results and convenient global parametrizations of all i o maps and all disturbance to output maps achievable for a given plant by a stabilizing compensator these parametrizations are then used to show that any such i o map and any such disturbance to output map may be simultaneously realized by choice of an appropriate controller in the special case of lumped systems it is shown that the design theory can be reduced to manipulations involving polynomial matrices only the resulting design procedure is thus shown to be more efficient computationally finally the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting it is shown that the classical results on asymptotic tracking can be generalized to this setting additionally sufficient conditions for robustness of asymptotic tracking and robustness of stability are developed

a lotka volterra cooperating reaction diffusion system with degenerate density dependent diffusion abstract in the lotka volterra cooperating reaction diffusion system if the diffusion coefficients are constants then for a certain set of reaction rates in the reaction function the solution of the system blows up in finite time and for another set of reaction rates a unique global solution exists and converges to the trivial solution however if the diffusion coefficients are density dependent then the dynamic behavior of the solution can be quite different the aim of this paper is to investigate the global existence and the asymptotic behavior of the solution for a class of density dependent cooperating reaction diffusion systems where the diffusion coefficients are degenerate it is shown that the time dependent problem has a unique bounded global solution and in addition to the trivial and semi trivial solutions the corresponding steady state problem has a positive maximal solution and a positive minimal solution moreover the time dependent solution converges to the maximal solution for one class of initial functions and to the minimal solution for another class of initial functions the above convergence property holds true for any reaction rates in the reaction function applications of the above results are given to a porous medium type of reaction diffusion problem as well as other types of diffusion coefficients including the finite sum and products of these functions

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given