control issues for the beverton holt equation in ecology by locally monitoring the environment carrying capacity non adaptive and adaptive cases this paper proposes a control algorithm to govern the solution of the beverton holt equation bhe under the potentially presence of additive disturbances the bhe to be controlled is defined by certain intrinsic growth rate and environment carrying capacity sequences the last one being susceptible of local modifications around nominal values in fact the control action provides the carrying capacity which makes that the solution of the current bhe tracks a reference sequence given by another bhe defined by appropriate intrinsic growth rate and environment carrying capacity sequences in this context the fact that the inverse of the bhe is a discrete time varying linear system is taken into account where the inverse of the carrying capacity sequence plays the role of control sequence the current and the reference bhes have to be close enough to each other in order that local modifications of the carrying capacity be able to meet the tracking objective a feedback control law is designed to achieve such an objective with a zero tracking error in the ideal case of known intrinsic growth rate sequence and no presence of disturbances an adaptive control law with the associated parameter estimation algorithm is considered when the intrinsic growth rate is fully or partially unknown and disturbances are present such a control strategy guarantees a bounded tracking error with the error converging asymptotically to zero in case that additive disturbances also converge to zero some results obtained from a simulation example illustrate the effectiveness of this control strategy

controllability is not necessary for adaptive pole placement control the key issue for adaptive pole placement control of linear time invariant systems is the possible singularity of the sylvester matrix corresponding to the coefficient estimate however to overcome the difficulty the estimate is modified by several methods which are either nonrecursive and with high computational load or recursive but with random search involved all of the previous works are done under the assumption that the system is controllable this paper gives the necessary and sufficient condition which is weaker than controllability for the system to be adaptively stabilizable first a nonrecursive algorithm is proposed to modify the estimates and the algorithm is proved to terminate in finitely many steps then with the help of stochastic approximation a recursive algorithm is proposed for obtaining the modification parameters it is proved that these modification parameters turn out to be a constant vector in a finite number of steps this leads to the convergence of the modified coefficient estimates for both algorithms the sylvester matrices corresponding to the modified coefficient estimates are asymptotically uniformly nonsingular thus the adaptive pole placement control problem can be solved i e the system can be adaptively stabilized

a globally convergent pole placement indirect adaptive controller a pole displacement indirect adaptive control algorithm is discussed for discrete time linear deterministic plants with arbitrary zeros the global convergence of the resulting closed loop control system is achieved subject to the assumptions that the plant order and a nonzero lower bound on its degree of controllability are known the problem of controllability of the plant model estimate is handled by using both a parameter correction and time varying nonlinear feedback a key property of the algorithm is that the plant estimate reaches a reasonable degree of controllability in a finite time after which the parameter correction and the nonlinear feedback are no longer used

stable adaptive regulation of arbitrary nth order plants this paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single input single output linear time invariant plant which is controllable and observable of known order n and has unknown parameters no further assumptions are made no external probing signal is required

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

brief paper on linear co positive lyapunov functions for sets of linear positive systems in this paper we derive necessary and sufficient conditions for the existence of a common linear co positive lyapunov function for a finite set of linear positive systems both the state dependent and arbitrary switching cases are considered our results reveal an interesting characterisation of linear stability for the arbitrary switching case namely the existence of such a linear lyapunov function can be related to the requirement that a number of extreme systems are metzler and hurwitz stable examples are given to illustrate the implications of our results

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

brief paper stability of switched positive linear systems with average dwell time switching in this paper the stability analysis problem for a class of switched positive linear systems splss with average dwell time switching is investigated a multiple linear copositive lyapunov function mlclf is first introduced by which the sufficient stability criteria in terms of a set of linear matrix inequalities are given for the underlying systems in both continuous time and discrete time contexts the stability results for the splss under arbitrary switching which have been previously studied in the literature can be easily obtained by reducing mlclf to the common linear copositive lyapunov function used for the system under arbitrary switching those systems finally a numerical example is given to show the effectiveness and advantages of the proposed techniques

brief paper on the stabilizability condition in indirect adaptive control many recent studies on overall stability of adaptive control systems require among other conditions that the identified model be stabilizable at least asymptotically in fact the usual identification methods do not guarantee this property in the passive approach without exciting extra signals or if the model order is subject to over estimation in order to solve this problem it is shown in this paper that certain classical identification algorithms can be easily modified in order to ensure the above stabilizability condition without affecting the other properties

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

solvability of static output feedback stabilization for lti positive systems abstract this paper addresses the stabilization problem of positive linear systems which have nonnegative states whenever the initial conditions are nonnegative the synthesis of static output feedback controllers that ensure the positivity and asymptotic stability of the closed loop system is investigated it is shown that this important problem is completely solved for single input and single output positive systems the proposed approach can be applied to multi input positive systems with controllers having one rank gains all the provided conditions are necessary and sufficient and can be solved in terms of linear programming

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

robust adaptive control of discrete nominally stabilizable plants this paper presents an indirect pole placement based adaptive control scheme for discrete linear time invariant non necessarily inversely stable and stabilizable systems the scheme is a pole placement type without requiring the plant inverse stability assumption the control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal given by an arbitrary stable filter under a bounded tracking error while ensuring robust closed loop stability the adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and possibly bounded disturbances are proved without assuming the controllability of the modeled plant a normalized least squares algorithm with a relative adaptation dead zone and a posteriori modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit such a property is crucial to solve the stable pole placement problem on the other hand the relative adaptation dead zone is included for robustness purposes under unmodeled dynamics and possibly bounded disturbances

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

adaptive control of a class of slowly time varying plants abstract an adaptive control system of the type considered earlier by the author which is designed to be stable under the assumption that the unknown plant parameters are constant is shown to maintain stability when the plant parameters are slowly time varying

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

stable discrete adaptive control with unknown high frequency gain this note presents a globally stable adaptive control algorithm applicable to discrete time single input single output linear time invariant systems a priori knowledge of neither the sign of the system s high frequency gain nor an upper bound on its magnitude is needed to prove global stability

stabilization of positive linear systems we consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant the existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane this allows to transform the problem to the stabilization problem of compartmental systems which is known and for which a solution has been proposed already we provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback a class of stabilizing feedbacks is given explicitly

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response

adaptive pole placement without excitation probing signals this paper presents an indirect adaptive control scheme for linear systems which may possibly be a nonminimum phase the control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters the system order is the only a priori knowledge required on the plant the adaptive control law is free from singularities in the sense that the estimated plant model is always controllable the singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties the analysis of the stability and the global convergence of a closed loop system is given in detail for both discrete time and continuous time systems

global boundedness of discrete time adaptive control just using estimator projection in this paper we study a discrete time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module this adaptive control algorithm does not involve modifications like data normalization use of deadzones or injection of persistently excited signals also it requires no a priori knowledge of system modelling errors it is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics the problem of indirect decentralized adaptive control of interconnected systems is also considered we use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems we show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions reference inputs disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

on the stability of positive linear switched systems under arbitrary switching laws we consider n dimensional positive linear switched systems a necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is hurwitz several researchers conjectured that for positive linear switched systems this condition is also sufficient recently gurvits shorten and mason showed that this conjecture is true for the case n 2 but is not true in general their results imply that there exists some minimal integer np such that the conjecture is true for all n np but is not true for n np we show that np 3

analysis of a new algorithm for continuous time robust adaptive control analysis of a robust indirect adaptive control scheme is presented it is shown that a new dead zone technique can be used so that the knowledge of the parameters of the upper bounding function on the unmodeled dynamics and the disturbance is not necessarily required furthermore the allowable unmodeled dynamics could be enlarged if the knowledge of the upper bound of the unmodeled dynamics is given

robust stabilization of a class of polytopic linear time varying continuous systems under point delays and saturating controls abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays under saturating state feedback controls the matrices describing the state space dynamics and control belong to polytopes also the controller gain matrix is characterized as belonging to another polytope whose vertices are computed from the knowledge of a closed bounded ball containing a set of values of the state norm and also the component wise saturating gains and saturation parameterizations this knowledge defines the polytope vertices through scaling diagonal matrices being associated with the various operation modes in the linear and saturated zones of each input component in these conditions the resulting closed loop system is of polytopic nature whose whole number of vertices is at most equal to the product of both numbers of vertices of the above two polytopes characterizing the plant parameterization and the saturation the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing candidates for each vertex of the polytopic closed loop system each satisfying in the most general case a riccati matrix differential inequality some conditions guaranteeing the stability conditions are obtained from a general kalman yakubovitch popov kyp lemma and some weaker stability conditions are also obtained for the time invariant case from a set of linear matrix inequalities associated with the set of vertices