global stabilization for a class of switched nonlinear feedforward systems abstract the problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper based on the integrator forwarding technique and the common lyapunov function method we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed loop system a common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

closed loop stabilization of planar bilinear switched systems in this paper we address the closed loop switched stabilization problem for planar bilinear systems under the assumption that the control is one dimensional and takes only the values 0 and 1 we construct a class of state static memoryless stabilizing feedback laws which preserve the properties of open loop switching signals in order to prove the stability of the implemented system we use lyapunov techniques for differential equations with discontinuous righthand side finally we point out some possible extensions of our result and compare it with related results previously proven by other authors

analysis and control of switched linear systems via dwell time min switching abstract this paper addresses analysis and switching control problems of switched linear systems to this end a mixed time driven and state dependent switching strategy is proposed it guarantees an average dwell time even when all subsystems are unstable the switching rule and its associated switching output feedback controllers are designed to stabilize the switched system and satisfy a weighted l 2 gain performance the proposed analysis and switching control approach could refrain frequent switches commonly observed in min switching based designs the effectiveness of the proposed approach has been illustrated through a spherical inverted pendulum example

on the value functions of the discrete time switched lqr problem in this paper we derive some important properties for the finite horizon and the infinite horizon value functions associated with the discrete time switched lqr dslqr problem it is proved that any finite horizon value function of the dslqr problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the so called switched riccati mapping it is also shown that under some mild conditions the family of the finite horizon value functions is homogeneous of degree 2 is uniformly bounded over the unit ball and converges exponentially fast to the infinite horizon value function the exponential convergence rate of the value iterations is characterized analytically in terms of the subsystem matrices

almost maximal growth of the hilbert function abstract let a s j be a standard artinian graded algebra over the polynomial ring s a theorem of macaulay dictates the possible growth of the hilbert function of a from any degree to the next and if this growth is the maximal possible then strong consequences have been given by gotzmann it can be phrased in terms of the base locus of the linear system defined by the relevant component s of j if j is the artinian reduction of the ideal of a finite set of points in projective space then this maximal growth for a was shown by bigatti geramita and the second author to imply strong geometric consequences for the points we now suppose that the growth of the hilbert function is one less than maximal this again has not as strong consequences for the base locus defined by the relevant component and when j is the artinian reduction of the ideal of a finite set of points in projective space we prove that almost maximal growth again forces geometric consequences

discrete time hybrid control in borel spaces average cost optimality criterion abstract this paper addresses an optimal hybrid control problem in discrete time with borel state and action spaces by hybrid we mean that the evolution of the state of the system may undergo deep changes according to structural modifications of the dynamic such modifications occur either by the position of the state or by means of the controller s actions the optimality criterion is of a long run ratio average or ratio ergodic type we provide the existence of optimal average policies for this hybrid control problem by analyzing an associated dynamic programming equation we also show that this problem can be translated into a standard or non hybrid optimal control problem with cost constraints besides we show that our model includes some special and important families of control problems such as those with an impulsive or switching mode finally to illustrate our results we provide an example on a pollution accumulation problem

on switching h controllers for a class of linear parameter varying systems abstract we consider switching h controllers for a class of linear parameter varying lpv systems scheduled along a measurable parameter trajectory the candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable we provide sufficient conditions to guarantee the stability of the switching lpv systems in terms of the dwell time and the average dwell time our results are illustrated with an example where switching between two robust controllers is performed for an lpv system

on switching stabilizability for continuous time switched linear systems this technical note studies switching stabilization problems for continuous time switched linear systems we consider four types of switching stabilizability defined under different assumptions on the switching control input the most general switching stabilizability is defined as the existence of a measurable switching signal under which the resulting time varying system is asymptotically stable discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length in addition we define feedback stabilizability in filippov sense respectively sample and hold sense as the existence of a feedback law under which closed loop filippov solution respectively sample and hold solution is asymptotically stable it is proved that the four switching stabilizability notions are equivalent and their sufficient and necessary condition is the existence of a piecewise quadratic control lyapunov function that can be expressed as the pointwise minimum of a finite number of quadratic functions

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

an lmi approach for h analysis and control of discrete time piecewise affine systems in this paper we investigate some analysis and control problems for discrete time hybrid systems in the piece wise affine form by using arguments from the dissipativity theory for non linear systems we show that h x analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system in this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

infinite horizon switched lqr problems in discrete time a suboptimal algorithm with performance analysis this paper studies the quadratic regulation problem for discrete time switched linear systems dslqr problem on an infinite time horizon a general relaxation framework is developed to simplify the computation of the value iterations based on this framework an efficient algorithm is developed to solve the infinite horizon dslqr problem with guaranteed closed loop stability and suboptimal performance due to these guarantees the proposed algorithm can be used as a general controller synthesis tool for switched linear systems

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

extended invariance principle for nonautonomous switched systems stability analysis is developed for nonlinear nonautonomous switched systems trajectories of which admit generally speaking a nonunique continuation on the right for these systems krasovskii lasalle s invariance principle is extended in such a manner to remain true even in the nonautonomous case in addition to a nonsmooth lyapunov function with negative semidefinite time derivatives along the system trajectories the extended invariance principle involves a coupled indefinite function to guarantee asymptotic stability of the system in question as an illustration of the capabilities of this principle a switched regulator of a fully actuated manipulator with frictional joints is constructed

necessary and sufficient conditions for regional stabilisability of second order switched linear systems with a finite number of subsystems in this paper the switching stabilisation problem of second order switched linear systems is studied by extending the best case switching signal bcss criteria for second order switched linear systems with two subsystems to the general case with any finite number of subsystems necessary and sufficient conditions for regional stabilisability of second order switched linear systems with any finite number of subsystems are proposed in this paper the main idea of this paper is to divide all the subsystems in a region into two groups based on their trajectory directions in that region by comparing pairwise the most stable subsystem for each group in a region can be determined and the bcss analysis among all the subsystems in that region is reduced to the bcss analysis between the two most stable subsystems in that region

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

an integral type multiple lyapunov functions approach for switched nonlinear systems an integral type multiple lyapunov functions mlfs approach for switched nonlinear systems is set up for the first time which gives a more general condition for analyzing the behavior of switched nonlinear systems since the branicky s nonincreasing condition is no longer assumed and the generalized mlfs condition is a special case of the condition provided meanwhile based on the integral type mlfs approach global stabilization for a class of switched nonlinear systems in p normal form is achieved by constructing state feedback controllers of subsystems and a proper switching law where the solvability of the problem under study for individual subsystems is not assumed two examples are also provided to demonstrate the effectiveness of the proposed design method

global stabilisation of switched nonlinear systems in p normal form with mixed odd and even powers this article investigates the problem of global stabilisation for a class of switched nonlinear systems in p normal form whose subsystems are not assumed to be asymptotically stabilisable unlike the existing results on systems in p normal form where the power order is only positive odd integer we allow positive even integer of the power order using the convex combination method and the adding a power integrator technique we construct a switching law and design state feedback controllers of individual subsystems explicitly by a recursive design algorithm to guarantee asymptotic stability of the closed loop system the designed method is also extended to the global stabilisation problem of switched nonlinear systems in p normal form with zero dynamics as an application of the proposed design method a continuously stirred tank reactor is studied

on non selective harvesting of a multispecies fishery incorporating partial closure for the populations highlightswe describe a prey predator fishery model incorporating partial closure for the populations the criterion for the existence of interior equilibrium point local and global stability of the system are derived the existence of bionomic equilibrium is discussed the optimal system is derived and solved numerically using an iterative method with runge kutta fourth order scheme numerical simulations are carried out to verify the analytically proved results a prey predator type fishery model incorporating partial closure for the populations is described in this paper the proposed model deals with a problem of non selective harvesting of a prey predator system in which both the prey and the predator species obey logistic law of growth the predator dependent beddington deangelis type functional response is taken into consideration dynamic behavior of the system is analyzed partial closure for the populations is considered as a controlling instrument to regulate the harvesting of the populations a dynamic framework towards the optimal utilization of the resource is developed using pontryagin s maximum principle the optimal system is numerically solved using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem results are analyzed with the help of graphical illustrations

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

on the first infinitesimal neighborhood of a linear configuration of points in p2 abstract we consider the following open questions fix a hilbert function h that occurs for a reduced zero dimensional subscheme of p 2 among all subschemes x with hilbert function h what are the possible hilbert functions and graded betti numbers for the first infinitesimal neighborhood z of x i e the double point scheme supported on x is there a minimum h min and maximum h max such function the numerical information encoded in h translates to a type vector which allows us to find unions of points on lines called linear configurations with hilbert function h we give necessary and sufficient conditions for the hilbert function and graded betti numbers of the first infinitesimal neighborhoods of all such linear configurations to be the same even for those h for which the hilbert functions or graded betti numbers of the resulting double point schemes are not uniquely determined we give one depending only on h that does occur we prove the existence of h max in general and discuss h min our methods include liaison techniques

delay induced oscillation in predator prey system with beddington deangelis functional response abstract the beddington deangelis predator prey system with distributed delay is studied in this paper at first the positive equilibrium and its local stability are investigated then with the mean delay as a bifurcation parameter the system is found to undergo a hopf bifurcation the bifurcating periodic solutions are analyzed by means of the normal form and center manifold theorems finally numerical simulations are also given to illustrate the results

on the uniformity of zero dimensional complete intersections abstract after showing that the general cayley bacharach conjecture formulated by d eisenbud m green and j harris 1996 6 is equivalent to a conjecture about the region of uniformity of a zero dimensional complete intersection we prove this conjecture in a number of special cases in particular after splitting the conjecture into several intervals we prove it for the first the last and part of the penultimate interval moreover we generalize the uniformity results of j hansen 2003 12 and l gold j little and h schenck 2005 9 to level schemes and apply them to obtain bounds for the minimal distance of generalized reed muller codes

control co design for discrete time switched linear systems the paper deals with the co design of a control policy composed by both the state feedback and the switching control law for discrete time switched linear systems constructive conditions are given that are necessary and sufficient for the stabilizability of systems which are periodic stabilizable the conditions are in form of a linear matrix inequality lmi problem whose solution provides the switching law and a family of state feedback gains stabilizing the system as well as a bound on the exponential decreasing rate the effectiveness of the proposed technique is illustrated by comparison with results from the literature

hilbert functions and level algebras abstract the authors consider certain quotients a r i of the polynomial ring r k x1 xr over an arbitrary field k they first determine upper and lower bounds on the hilbert functions of any algebra having the form a r v where v is the largest ideal of r agreeing in degrees at least j with the ideal v generated by a vector subspace v rj of degree j forms these bounds extend the macaulay bounds theorem 1 4 a level artinian quotient of a r i has socle soc a 0 m m x1 xr in a single degree j the authors next determine the extremal hilbert functions hmax t j r and hmin t j r that occur for level graded artin algebra quotients of r having socle degree j and type t dimk soc a and they describe the extremal strata theorem 1 8 they next give a natural upper bound for the hilbert function of level algebra quotients of the coordinate ring o z of a punctual subscheme z p n n r 1 in terms of the hilbert function h z and j t this bound was known and known to be sharp in the case z is locally gorenstein and t 1 finally they show that there are no level algebras of hilbert function t 1 3 4 5 6 2 proposition 2 7 given that there are smooth punctual subschemes z of p 2 with hilbert function h z 1 3 4 5 6 6 this result shows that the sharpness of the natural upper bound in the case where z is gorenstein and t 1 does not extend to level algebra quotients of type 2 even when z is smooth the extremality results for the hilbert functions of level algebras and some counterexamples use the extremality theorem of f h s macaulay 1927 proc london math soc 26 531 555 and g gotzmann s 1978 math z 158 61 70 results on the hilbert scheme

necessary and sufficient conditions for regional stabilisability of generic switched linear systems with a pair of planar subsystems in this article the regional stabilisability issues of a pair of planar lti systems are investigated through the geometrical approach and easily verifiable necessary and sufficient conditions are derived the main idea of the article is to characterise the best case switching signals based upon the variations of the constants of the integration of the subsystems the conditions are generic as all possible combinations of the subsystem dynamics are considered

global dynamics and bifurcation in a stage structured prey predator fishery model with harvesting abstract this paper describes a prey predator model with stage structure for predator and selective harvesting effort on predator population the holling type ii functional response function is taken into consideration all the equilibria of the proposed system are determined and the behavior of the system is investigated near them local stability of the system is analyzed geometric approach is used to derive the sufficient conditions for global stability of the system the occurrence of hopf bifurcation of the model system in the neighborhood of the co existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource pontryagin s maximum principle is used to characterize the optimal control the optimal system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

hopf bifurcation and global stability for a delayed predator prey system with stage structure for predator abstract in this paper a delayed predator prey system with stage structure for predator is proposed and studied it is found that the time delay is harmless for permanence of the stage structured system if 1 we show that the unique positive equilibrium is locally asymptotically stable when time delay is sufficiently small while loss of stability by a hopf bifurcation can occur as the delay increases

the gotzmann coefficients of hilbert functions abstract in this paper we investigate some algebraic and geometric consequences which arise from an extremal bound on the hilbert function of the general hyperplane section of a variety green s hyperplane restriction theorem these geometric consequences improve some results in this direction first given by green and extend others by bigatti geramita and migliore other applications of our detailed investigation of how the hilbert polynomial is written as a sum of binomials are to conditions that must be satisfied by a polynomial if it is to be the hilbert polynomial of a non degenerate integral subscheme of p n a problem posed by r p stanley we also give some new restrictions on the hilbert function of a zero dimensional reduced scheme with the uniform position property

stabilization of switched systems via composite quadratic functions this paper investigates stabilization of switched systems by using a lyapunov function composed of a family of continuously differentiable functions switching laws are constructed by using the directional derivatives along the trajectories of the subsystems conditions for stabilization are established with careful consideration of sliding modes and directional derivatives along sliding modes three types of composite quadratic lyapunov functions the max of quadratics the min of quadratics and the convex hull of quadratics are used for deriving matrix conditions of stabilization and for constructing switching laws dual stabilization results are established with respect to the pair of conjugate lyapunov functions the max of quadratics and the convex hull of quadratics conditions of stabilization are derived as bilinear matrix inequalities and solved with lmi based numerical tools relationship between the newly derived conditions and some existing conditions are investigated it is observed that the min of quadratics which is nondifferentiable and nonconvex may be a more convenient tool than the other two types of functions which are convex and or differentiable numerical examples are used to demonstrate the synthesis results and the advantage of the composite quadratic functions over existing multiple lyapunov functions in particular better results have been obtained when the number of quadratic functions is greater than the number of subsystems

graph lyapunov function for switching stabilization and distributed computation abstract this paper studies stabilization of discrete time switched linear systems slss using the notion of graph control lyapunov functions gclfs a gclf is a set of lyapunov functions defined on a weighted digraph where each lyapunov function is represented by a node in the digraph and there is a lyapunov inequality associated with each subgraph consisting of a node and its out neighbors the weight of a directed edge indicates the decay or growth rate of the lyapunov functions it is proved that an sls is switching stabilizable if and only if there exists a gclf the main benefits of gclfs are reduced computational cost and conservatism for stabilizability tests besides we show that the proposed gclf framework unifies several control lyapunov functions and the related stabilization theorems moreover we propose a distributed algorithm to evaluate the stabilizability with reduced computational costs by taking benefits of the graph structure of gclfs several examples are given to demonstrate the efficiency of the algorithm

optimal control of switching systems this paper considers an optimal control problem for a switching system for solving this problem we do not make any assumptions about the number of switches nor about the mode sequence they are determined by the solution of the problem the switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter it is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system the relationship between the two sets of trajectories 1 motivates the shift of focus from the original problem to the more general one and 2 underlies the engineering relevance of the study of the second problem sufficient and necessary conditions for optimality are formulated for the second optimization problem if they exist bang bang type solutions of the embedded optimal control problem are solutions of the original problem otherwise suboptimal solutions are obtained via the chattering lemma

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

exponential stabilization of discrete time switched linear systems this article studies the exponential stabilization problem for discrete time switched linear systems based on a control lyapunov function approach it is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control lyapunov function such a converse control lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic lyapunov functions for convenience or heuristic reasons in addition it is also proved that if a switched linear system is exponentially stabilizable then it must be stabilizable by a stationary suboptimal policy of a related switched linear quadratic regulator lqr problem motivated by some recent results of the switched lqr problem an efficient algorithm is proposed which is guaranteed to yield a control lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

linear quadratic regulation of switched systems using informed policies the problem of designing a switching and control policy for regulating the state of a switched linear system to zero while minimizing a quadratic cost appears in numerous applications however obtaining the optimal policy is in general computationally intractable here we propose a class of suboptimal policies that exploit information in terms of upper or lower bounds on the optimal cost we analyze the performance of these novel policies obtaining new bounds on the optimal cost which are tighter than the initial ones the usefulness of these policies and performance bounds is illustrated in the context of resource aware control

on the identifiability of ternary forms abstract we describe a new method to determine the minimality and identifiability of a waring decomposition a of a specific form symmetric tensor t in three variables our method which is based on the hilbert function of a can distinguish between forms in the span of the veronese image of a which in general contains both identifiable and not identifiable points depending on the choice of coefficients in the decomposition this makes our method applicable for all values of the length r of the decomposition from 2 up to the generic rank a range which was not achievable before though the method in principle can handle all cases of specific ternary forms we introduce and describe it in details for forms of degree 8

on the genus and hartshorne rao module of projective curves in this paper optimal upper bounds for the genus and the dimension of the graded components of the hartshorne rao module of curves in projective n space are established this generalizes earlier work by hartshorne h and martin deschamps and perrin mdp special emphasis is put on curves in bf p 4 the first main result is a so called restriction theorem it says that a non degenerate curve of degree d geq 4 in bf p 4 over a field of characteristic zero has a non degenerate general hyperplane section if and only if it does not contain a planar curve of degree d 1 see th 1 3 then using methods of brodmann and nagel bounds for the genus and hartshorne rao module of curves in bf p n with non degenerate general hyperplane section are derived it is shown that these bounds are best possible in a very strict sense coupling these bounds with the restriction theorem gives the second main result for curves in bf p 4 then curves of maximal genus are investigated the betti numbers of their minimal free resolutions are computed and a description of all reduced curves of maximal genus in bf p n of degree geq n 2 is given finally all pairs d g of integers which really occur as the degree d and genus g of a non degenerate curve in bf p 4 are described

dynamic programming for constrained optimal control of discrete time linear hybrid systems in this paper we study the solution to optimal control problems for constrained discrete time linear hybrid systems based on quadratic or linear performance criteria the aim of the paper is twofold first we give basic theoretical results on the structure of the optimal state feedback solution and of the value function second we describe how the state feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

mode identifying time estimation and switching delay tolerant control for switched systems in this paper an elementary time unit etu method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems the activation interval of a subsystem is considered to consist of a finite time number of segments called etus by which a novel class of time scheduled lyapunov function is used to estimate the admissible delay in mode identification for switched systems further the etu method is applied for switching delay tolerant control problem and a class of time scheduled state feedback controllers are designed to achieve the exponentially stability several numerical examples are presented to validate the theoretic findings

on the stabilizability of discrete time switched linear systems novel conditions and comparisons in this paper we deal with the stabilizability property for discrete time switched linear systems a recent necessary and sufficient characterization of stabilizability based on set theory is considered as the reference for comparing the computation oriented sufficient conditions the classical bmi conditions based on lyapunov metzler inequalities are considered and extended novel lmi conditions for stabilizability derived from the geometric ones are presented that permit to combine generality with computational affordability for the different conditions the geometrical interpretations are provided and the induced stabilizing switching laws are given the relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity

technical communique stabilizing controllers design for switched nonlinear systems in strict feedback form this paper considers the stabilization problem for a class of switched nonlinear systems under arbitrary switching based on the backstepping method and the control lyapunov function approach it is shown that under a simultaneous domination assumption a switched nonlinear system in strict feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller a universal formula for constructing stabilizing feedback laws is presented one example is included for verifying the obtained results

generalized input to state ell_2 gains of discrete time switched linear control systems a generalized notion of input to state ell 2 gain is proposed for discrete time switched linear control systems slcss dependent on a discount factor of subsystem matrices this generalized ell 2 gain provides new insight into input to state behaviors of the slcss under parameter variations after establishing analytical properties of the generalized ell 2 gain this paper focuses on the generating function approach to the study of the generalized ell 2 gain important properties of generating functions are derived and it is shown that their radii of convergence characterize the generalized ell 2 gain furthermore iterative algorithms are developed for computing the generating functions with proven uniform or exponential convergence numerical results show that these algorithms yield efficient estimates of both the generalized and classical ell 2 gains

feedback stabilization for multiinput switched nonlinear systems two subsystems case in this note based on the control lyapunov function approach a new method for solving the feedback stabilization problem of switched systems that are switching arbitrarily between two multiinput nonlinear subsystems is introduced necessary and sufficient conditions for the existence of globally uniformly asymptotically stabilizing state feedback controllers are derived additionally a universal formula for constructing implementable stabilizing controllers is given when the presented conditions hold one numerical example is given to illustrate the results

analysis on the existence of the steady states for an ecological mathematical model with predator prey dependent functional response abstract we establish a reaction diffusion ecological mathematical model with predator prey dependent functional response and the neumann boundary conditions first we study the bifurcation solution emitting from the unique positive constant solution by considering the local bifurcation finally we mainly analyze the coexistence of the prey and predator with the help of the fixed point index theory where we use a different approach in calculating one of the fixed point indices

h_ infty control of switched nonlinear systems in p normal form using multiple lyapunov functions the problem of h control of switched nonlinear systems in p normal form is investigated in this technical note where the solvability of the h control problem for individual subsystems is unnecessary using the generalized multiple lyapunov functions method and the adding a power integrator technique we design a switching law and construct continuous state feedback controllers of subsystems explicitly by a recursive design algorithm to produce global asymptotical stability and a prescribed h performance level multiple lyapunov functions are exploited to reduce the conservativeness caused by adoption of a common lyapunov function for all subsystems which is usually required when applying the backstepping like recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

exponential stability with l_ 2 gain condition of nonlinear impulsive switched systems in this technical note we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time varying disturbances by using the switched lyapunov function method sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained they ensure that the nonlinear impulsive switched systems are not only exponentially stable but also satisfy the l2 gain condition based on the stability results obtained an effective computational method is devised for the construction of switched linear stabilizing feedback controllers a numerical example is presented to illustrate the effectiveness of the results obtained

relaxing dynamic programming the idea of dynamic programming is general and very simple but the curse of dimensionality is often prohibitive and restricts the fields of application this paper introduces a method to reduce the complexity by relaxing the demand for optimality the distance from optimality is kept within prespecified bounds and the size of the bounds determines the computational complexity several computational examples are considered the first is optimal switching between linear systems with application to design of a dc dc voltage converter the second is optimal control of a linear system with piecewise linear cost with application to stock order control finally the method is applied to a partially observable markov decision problem pomdp

hybrid state feedback stabilization with l 2 performance for discrete time switched linear systems in this paper the co design of continuous variable controllers and discrete event switching logics both in state feedback form is investigated for a class of discrete time switched linear control systems it is assumed that none of the subsystems is stabilized through a continuous state feedback alone however it is possible to stabilize the whole switched system via carefully designing both the continuous controllers and the switching logics sufficient synthesis conditions for this co design problem are proposed here in the form of bilinear matrix inequalities which is based on the argument of multiple lyapunov functions the closed loop switched system forms a special class of linear hybrid system and is shown to be asymptotically stable with a finite l 2 induced gain

the weak and strong lefschetz properties for artinian k algebras abstract let a i 0ai be a standard graded artinian k algebra where chark 0 then a has the weak lefschetz property if there is an element l of degree 1 such that the multiplication l a i a i 1 has maximal rank for every i and a has the strong lefschetz property if l d a i a i d has maximal rank for every i and d the main results obtained in this paper are the following 1 every height three complete intersection has the weak lefschetz property our method surprisingly uses rank two vector bundles on p 2 and the grauert mulich theorem 2 we give a complete characterization including a concrete construction of the hilbert functions that can occur for k algebras with the weak or strong lefschetz property and the characterization is the same one 3 we give a sharp bound on the graded betti numbers achieved by our construction of artinian k algebras with the weak or strong lefschetz property and fixed hilbert function this bound is again the same for both properties some hilbert functions in fact force the algebra to have the maximal betti numbers 4 every artinian ideal in k x y possesses the strong lefschetz property this is false in higher codimension

homogeneous state feedback stabilization of homogenous systems we show that for any asymptotically controllable homogeneous system in euclidean space not necessarily lipschitz at the origin there exists a homogeneous control lyapunov function and a homogeneous possibly discontinuous state feedback law stabilizing the corresponding sampled closed loop system if the system satisfies the usual local lipschitz condition on the whole space we obtain semiglobal stability of the sampled closed loop system for each sufficiently small fixed sampling rate if the system satisfies a global lipschitz condition we obtain global exponential stability for each sufficiently small fixed sampling rate the control lyapunov function and the feedback are based on the lyapunov exponents of a suitable auxiliary system and admit a numerical approximation

on stabilizability of switched positive linear systems under state dependent switching this paper addresses the stabilization of switched positive linear systems by state dependent switching we show that if there is a hurwitz convex or linear combination of the coefficient matrices then the switched positive linear system can be exponentially stabilized by means of a single linear co positive lyapunov function if there is not a stable combination of system matrices it is shown that the exponential stabilizability is equivalent to a completeness condition on the coefficient matrices when the switched positive systems can not be stabilized by the single lyapunov function we provide a unified criterion for piecewise exponential stabilizability in terms of multiple linear co positive lyapunov functions

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

stabilisation of second order lti switched positive systems the stabilisation problem of second order switched positive systems consisting of two unstable subsystems is considered in this article by considering the vector fields and geometric characteristics a necessary and sufficient condition for the stabilisability of second order switched positive systems with two unstable subsystems is provided furthermore it is shown via this condition that neither second order switched positive systems consisting of two subsystems with unstable nodes nor second order switched positive systems consisting of one subsystem with unstable nodes and the other with a saddle point can be stabilised via any switching law

controllability analysis and control design for switched boolean networks with state and input constraints this paper investigates the controllability analysis and the control design for switched boolean networks sbns with state and input constraints by using the semi tensor product method and presents a number of new results on their controllability optimal control and stabilization first the constrained incidence matrix is proposed for sbns based on which several necessary and sufficient conditions are obtained for the controllability second using the results on the controllability two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed designed shortest termination time third the constrained sbn is converted to an equivalent unconstrained one based on which some necessary and sufficient conditions are presented for the stabilization of the constrained sbn with open loop and closed loop controls respectively finally a practical example of the apoptosis network is studied by using the new results obtained in this paper the s

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

finite valued feedback laws and piecewise classical solutions abstract often in engineering literature we find control systems in which the open loop inputs are piecewise constant and take values in a finite set such open loop inputs cause the system to have fairly regular solutions on the other hand when acting in closed loop feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type in fact pathological behaviours such as the accumulation of discontinuities may appear zeno phenomenon we give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviours

output feedback control for switched linear systems subject to actuator saturation this article is devoted to the output feedback control problem for switched linear systems subject to actuator saturation we consider both continuous and discrete time switched systems using the minimal switching rule nonlinear output feedbacks expressed in the form of quasi linear parameter varying system are designed to satisfy a pre specified disturbance attenuation level defined by the regional 2 l2 gains over a class of energy bounded disturbances the conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation a spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach

optimal linear quadratic regulator of switched systems this paper considers the optimal control problem of linear switched systems with linear quadratic lq cost or multiple lq cost by adopting an embedding transformation the switching design problem is relaxed and transformed into a traditional optimal control problem the bang bang type solutions of the embedded optimal control problems are obtained for both the positive definite lq cost case and the multiple lq cost case which are the optimal solutions to the original problems the switching sequence of modes and the switching instants can be calculated by solving a closed form optimal switching condition the optimal state feedback control law is determined simultaneously finally numerical results are provided to illustrate the effectiveness of the proposed method

existence of positive solutions for a prey predator model with refuge and diffusion abstract we are concerned with a prey predator reaction diffusion model with monotonic functional response and specific refuge size we discuss both existence and nonexistence of positive solutions of the model by using fixed point index theory and bifurcation theory as the main argument tools we also discuss bifurcation solutions of which stability is established by using spectrum analysis methods moreover we analyze the effects of refuge size on the dynamics of the model

generating functions of switched linear systems analysis computation and stability applications in this paper a unified framework is proposed to study the exponential stability of discrete time switched linear systems and more generally the exponential growth rates of their trajectories under three types of switching rules arbitrary switching optimal switching and random switching it is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong the weak and the mean generating functions respectively in particular necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence various properties of the generating functions are established and their relations are discussed algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

coexistence region and global dynamics of a harvested predator prey system the study of populational dynamics with harvesting is related to the optimal man agement of renewable resources in this paper we consider a predator prey model in which two ecologically interacting species are harvested independently with constant rates the main purpose of the present work is to offer a complete mathematical analysis for the model and to describe some of the significant qualitative results that may be expected to arise from the interplay of biological forces our study shows that the maximum safe harvest may be far less than what would be assumed from a local analysis for the equilibria it is also proved that the harvested predator prey system may exhibit very complicated dynamics such as a spontaneous appearance of a homoclinic orbit and multiple limit cycles

complete mathematical analysis of predator prey models with linear prey growth and beddington deangelis functional response the dynamics of a predator prey model with a beddington deangelis functional response and linear intrinsic growth rate of the prey population is fully analyzed conditions on local and global stability of the interior equilibrium are established the equilibria type are determined all possible global asymptotic behaviors of the system are considered including the determination of the extinction conditions and existence of periodic orbits it is shown that mutual interference between predators can alone stabilize predator prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model additional biological implications and a set of numerical simulations supporting the analysis are also presented

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

state feedback control of switched linear systems an lmi approach this paper addresses the problem of state feedback control of continuous time switched linear systems with arbitrary switching rules a quadratic lyapunov function with a common matrix is used to derive a stabilizing switching control strategy that guarantees i the assignment of all the eigenvalues of each linear subsystem inside a chosen circle in the left hand half of the complex plane ii a minimum disturbance attenuation level for the closed loop switched system the proposed design conditions are given in terms of linear matrix inequalities that encompass previous results based on quadratic stability conditions with fixed control gains although the quadratic stability based on a fixed lyapunov matrix has been widely used in robust control design the use of this condition to provide a convex design method for switching feedback gains has not been fully investigated numerical examples show that the switching control strategy can cope with more stringent design specifications than the fixed gain strategy being useful to improve the performance of this class of systems

analysis of predator prey models with continuous threshold harvesting abstract we formulate an alternative form of threshold harvesting and investigate its properties within the framework of a predator prey model our formulation accounts for economic constraints and is defined as a continuous harvesting function of the predator species theoretical and numerical analysis indicate that our formulation which we call continuous threshold policy ctp can help improve undesirable behavior of the predator prey ecosystem our study includes uniform boundedness of solutions stability of equilibria and periodic orbits bifurcations and heteroclinic orbits

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check

geometric consequences of extremal behavior in a theorem of macaulay f s macaulay gave necessary and sufficient conditions on the growth of a nonnegative integer valued function which determine when such a function can be the hilbert function of a standard graded k algebra we investigate some algebraic and geometric consequences which arise from the extremal cases of macaulay s theorem our work also builds on the fundamental work of g gotzmann our principal applications are to the study of hilbert functions of zeroschemes with uniformity conditions as a consequence we have new strong limitations on the possible hilbert functions of the points which arise as a general hyperplane section of an irreducible curve