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

an nth step set invariance approach to the analysis and design of discrete time linear systems subject to actuator saturation abstract for a discrete time linear system subject to actuator saturation an analysis and design approach based on n th step set invariance is proposed an n th step invariant set is a set from which all trajectories will enter a contractively invariant set in n steps and thus can be used as an estimate of the domain of attraction such an estimate is less conservative than an estimate obtained on the basis of contractive invariance of ellipsoids which excludes initial conditions from which the trajectories overshoot outside the ellipsoid before converging to the origin in comparison with the existing approach based on conventional set invariance the proposed approach results in a larger domain of attraction and better performance both in the analysis of the closed loop system under a given feedback gain and in the design of feedback gain in comparison with the saturated and nonsaturated sns invariant set approach which is an analysis approach the proposed approach can be used for control design even in the presence of plant uncertainties

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

further studies on h observer design for continuous time takagi sugeno fuzzy model abstract this brief paper is concerned with the problem of observer based h control for nonlinear systems presented by t s takagi sugeno fuzzy models the aim is to reduce the conservatism of finding a smaller h performance index by applying the non quadratic lyapunov function the one step lmis linear matrix inequalities method is applied to design the controller gains and observer gains in addition the initial positions of the observer states are also discussed and an optimization problem is solved to obtain new stable region in the end three examples are given to demonstrate the effectiveness of the proposed approach

multiple positive solutions for first order nonlinear integro differential equations in banach spaces by using the fixed point index theory the author obtains the existence of two positive solutions for a boundary value problem of first order nonlinear integro differential equations on an infinite interval in a real banach space

model predictive control for uncertain max min plus scaling systems in this paper we extend the classical min max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization minimization addition and scalar multiplication and that we call max min plus scaling mmps systems provided that the stage cost is an mmps expression and considering only linear input constraints then the open loop min max model predictive control problem for mmps systems can be transformed into a sequence of linear programming problems hence the min max model predictive control problem for mmps systems can be solved efficiently despite the fact that the system is non linear a min max feedback model predictive control approach using disturbance feedback policies is also presented which leads to improved performance compared to the open loop approach

robust h filtering for nonlinear systems abstract a robust or h approach to filtering for nonlinear systems is considered a bound on the estimate error as a function of the disturbance energy is obtained the corresponding dynamic programming equation is a first order pde this has computational ramifications the case where the measurements are discrete time is considered also a numerical method is discussed

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

guaranteed cost synchronization of chaotic cellular neural networks with time varying delay synchronization of cellular neural networks with time varying delay is discussed in this letter based on razumikhin theorem a guaranteed cost synchronous controller is given unlike lyapunov krasovskii analysis process there is no constraint on the change rate of time delay the saturated terms emerging in the razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by lipschitz condition and vector inequality which will bring more conservatism then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form with the help of a sufficient and necessary transformation condition the minimization of the guaranteed cost is studied and a further criterion for getting the controller is presented finally the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time varying delay cellular neural networks

analysis and design for delta operator systems with actuator saturation this paper studies the problem of estimating the domain of attraction for delta operator systems under a pre designed saturated linear feedback ellipsoids are used as the estimates of domain of attraction for delta operator systems a condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractive invariant moreover some necessary and sufficient conditions are given for single input delta operator systems the results are also further extended to determine the invariant sets for delta operator systems with persistent disturbances linear matrix inequalities based on the methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements some numerical examples are given to illustrate the effectiveness of the developed techniques

absolute stability with a generalized sector condition this paper generalizes the linear sector in the classical absolute stability theory to a sector bounded by concave convex functions this generalization allows more flexible or more specific description of the nonlinearity and will thus reduce the conservatism in the estimation of the domain of attraction we introduce the notions of generalized sector and absolute contractive invariance for estimating the domain of attraction of the origin necessary and sufficient conditions are identified under which an ellipsoid is absolutely contractively invariant in the case that the sector is bounded by piecewise linear concave convex functions these conditions can be exactly stated as linear matrix inequalities moreover if we have a set of absolutely contractively invariant aci ellipsoids then their convex hull is also aci and inside the domain of attraction we also present optimization technique to maximize the absolutely contractively invariant ellipsoids for the purpose of estimating the domain of attraction the effectiveness of the proposed method is illustrated with examples

multiple positive solutions of a m point boundary value problem for 2nth order singular integro differential equations in banach spaces abstract in this paper we obtain the existence of multiple positive solutions of a m point boundary value problem for 2 n th order singular nonlinear integro differential equations in a banach space by means of fixed point index theory of completely continuous operators

the existence of solutions of infinite boundary value problems for first order impulsive differential systems in banach spaces in this paper the existence of solutions of infinite boundary value problems for first order impulsive differential systems is obtained by means of the schauder fixed point theorem in a banach space

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

disturbance attenuation for systems with input saturation an lmi approach a new design technique is proposed to improve disturbance attenuation for systems with input saturation the main results rely on a multiobjective approach which combines the quadratic stabilization technique with constraints on inputs for the full state feedback problem the sufficient conditions for the feasibility of a high gain controller are expressed in terms of linear matrix inequalities lmi for output feedback design the controllers are assumed to have an observer based structure the sufficient conditions for the output feedback controller to recover the full state properties are also given in terms of lmi

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

h sub spl infin almost disturbance decoupling with internal stability for linear systems subject to input saturation for a linear system subject to input saturation and input additive disturbances we show that 1 the h sub spl infin almost disturbance decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system in the absence of saturation is stabilizable no matter where the open loop poles are and 2 the h sub spl infin almost disturbance decoupling problem with semiglobal asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left half plane the results generalize those in lin et al 1996 by not requiring the disturbance to be bounded by a known bound or even bounded

brief paper disturbance tolerance and rejection of linear systems with imprecise knowledge of actuator input output characteristics we study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics disturbances either bounded in energy or bounded in magnitude are considered the actuator input output characteristics are assumed to reside in a so called generalized sector bounded by piecewise linear curves robust bounded state stability of the closed loop system is first defined and characterized in terms of linear matrix inequalities lmis based on this characterization the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed loop system under a given feedback law is formulated into and solved as optimization problems with lmi constraints

brief paper l2 gain analysis for a class of switched systems this paper considers the problem of disturbance tolerance rejection for a family of linear systems subject to actuator saturation and l 2 disturbances for a given set of linear feedback gains a given switching scheme and a given bound on the l 2 norm of the disturbances conditions are established in terms of linear or bilinear matrix inequalities under which the resulting switched system is bounded state stable that is trajectories starting from a bounded set will remain inside the set or a larger bounded set with these conditions both the problem of assessing the disturbance tolerance rejection capability of the closed loop system and the design of feedback gain and switching scheme can be formulated and solved as constrained optimization problems disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories from a given set remain bounded disturbance rejection is measured by the restricted l 2 gain over the set of tolerable disturbances in the event that all systems in the family are identical the switched system reduces to a single system under a switching feedback law it will be shown that such a single system under a switching feedback law has stronger disturbance tolerance rejection capability than a single linear feedback law can achieve

regulator problem for linear continuous time systems with nonsymmetrical constrained control the regulator problem is studied for linear continuous time systems with nonsymmetrical constrained control necessary and sufficient conditions allowing the largest nonsymmetrical polyhedral positively invariant domain w r t the system in the closed loop to be obtained are given the case of symmetrical constrained control is obtained as a particular case

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

analysis of linear systems in the presence of actuator saturation and l2 disturbances this paper presents a method for the analysis and control design of linear systems in the presence of actuator saturation and l 2 disturbances a simple condition is derived under which trajectories starting from an ellipsoid will remain inside an outer ellipsoid the stability and disturbance tolerance rejection ability of the closed loop system under a given feedback law is measured by the size of these two ellipsoids and the difference between them based on the above mentioned condition the problem of estimating the largest inner ellipsoid and or the smallest difference between the two ellipsoid is then formulated as a constrained optimization problem all the constraints are shown to be equivalent to lmis in addition disturbance rejection ability in terms of l 2 gain is also determined by the solution of an lmi optimization problem by viewing the feedback gain as an additional free parameter the optimization problem can easily be adapted for controller design numerical examples show that the proposed analysis and design methods significantly improve recent results on the same problems

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

analysis and design of singular linear systems under actuator saturation and l2 l disturbances abstract this paper carries out an analysis of the l 2 gain and l performance for singular linear systems under actuator saturation the notion of bounded state stability bss with respect to the influence of l 2 or l disturbances is introduced and conditions under which a system is bounded state stable are established in terms of linear matrix inequalities lmis the disturbance tolerance capability of the system is then measured as the bound on the l 2 or l norm of the disturbances under which the system remains bounded state stable and the disturbance rejection capability is measured by the restricted l 2 gain from the disturbance to the system output or l norm of the system output based on the bss conditions assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as lmi constrained optimization problems by viewing the feedback gain as an additional variable these optimization problems can be readily adapted for control design our analysis and design reduce to the existing results for regular linear systems in the degenerate case where the singular linear system reduces to a regular system and to the existing results for singular systems in the absence of actuator saturation or when the disturbance is weak enough to not cause saturation

infinite boundary value problems for nth order nonlinear impulsive integro differential equations in banach spaces abstract in this paper the existence of unbounded nonnegative solutions of a boundary value problem for n th order impulsive integro differential equations on an infinite interval in banach spaces is obtained by means of the monch fixed point theory in a banach space

on optimization of stochastic maxmin plus scaling systemsan approximation approach a large class of discrete event and hybrid systems can be described by a maxmin plus scaling mmps model i e a model in which the main operations are maximization minimization addition and scalar multiplication accordingly optimization of mmps systems appears in different problems defined for discrete event and hybrid systems for a stochastic mmps system this optimization problem is computationally highly demanding as often numerical integration has to be used to compute the objective function the aim of this paper is to decrease such computational complexity by applying an approximation method that is based on the moments of a random variable and that can be computed analytically

mpc for continuous piecewise affine systems abstract a large class of hybrid systems can be described by a max min plus scaling mmps model i e using the operations maximization minimization addition and scalar multiplication first we show that continuous piecewise affine systems are equivalent to mmps systems next we consider model predictive control mpc for these systems in general this leads to nonlinear nonconvex optimization problems we present a new mpc method for mmps systems that is based on canonical forms for mmps functions in case the mpc constraints are linear constraints in the inputs only this results in a sequence of linear optimization problems such that the mpc control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

discrete event systems with stochastic processing times discrete event dynamic systems are studied in which the underlying algebra is the max algebra and the coefficients in the system referring to processing times in practice are stochastic the processing times and or the transportation times within a network show stochastic fluctuations the restrictions are that the stochastic processing times of the nodes in the network are independent and identically distributed the asymptotic behavior of the system is investigated and the average duration of one cycle of the process is calculated a specific example of the theory is considered the state space is two dimensional and the probability distributions are exponential it is shown that the process approaches a stationary limit as time proceeds the case when the probability distributions are discrete is also treated several examples are given two dimensional systems and more generally finite dimensional systems are considered

minimal nonnegative solutions for nth order integro differential equations in banach spaces1this research work was supported by the national natural science foundation of china and the doctoral program foundation of the state education commission of china 1 in this paper the cone theory and monotone iterative technique are used to investigate the minimal nonnegative solutions of initial value problems ivps for nth order nonlinear integro differential equations of mixed type on an infinite interval in a banach space