further results on global stabilization of discrete nonlinear systems in this paper we show how recent advances 11 12 in global stabilization of continuous time nonaffine nonlinear systems with stable free dynamics can be nontrivially generalized to their discrete time counterparts by means of passivity and bounded state feedback as a consequence global stabilization results of discrete time nonlinear systems with triangular structure are established

a generalization of polyak s convergence result for subgradient optimization this paper generalizes a practical convergence result first presented by polyak this new result presents a theoretical justification for the step size which has been successfully used in several specialized algorithms which incorporate the subgradient optimization approach

smooth output feedback stabilization of planar systems without controllable observable linearization this note considers the problem of global stabilization by output feedback for a family of planar systems whose jacobian linearization is neither controllable nor observable the problem cannot be dealt with by existing output feedback design methods most of them are based on the separation principle under appropriate growth conditions we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization the novelty of our control scheme lies in the explicit design of a dynamic output compensator which combines a nonlinear gain observer design and the technique of adding a power integrator as a consequence an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form which turns out to be new even in the two dimensional case

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

a cross decomposition algorithm for capacitated facility location we present an implementation of the cross decomposition method to solve the capacitated facility location problem the method unifies benders decomposition and lagrangean relaxation into a single framework that involves successive solutions to a transportation problem and a simple plant location problem computational tests on problems with as many as 100 candidate facility locations and 200 customers provide evidence that the approach is superior to several other methods the specialized cross decomposition program is on a common set of test problems about ten times faster than several recently developed programs we also present a simple algorithm to strengthen benders cuts

on asymptotic stabilization of driftless systems a simple approach is proposed to investigate the stabilization of driftless systems by taking the control input as a function of system states we can transform the stabilization design into a stability problem the known stability results on the nonlinear autonomous system are then employed to derive the asymptotically stabilizing controllers by solving an algebraic equation existence conditions of the asymptotic stabilizing feedback controller for the driftless systems by employing the stability criteria on linear systems and a class of third order homogeneous systems are obtained to demonstrate the application of the approach

kyp lemma state feedback and dynamic output feedback in discrete time bilinear systems abstract this paper shows how a generalization of the kalman yacubovitch popov kyp lemma can be built for discrete time bilinear passive systems and how the concepts of passivity and feedback equivalence can be applied to solve the problem of global stabilization via smooth state feedback bounded state feedback and dynamic output feedback for a class of discrete time bilinear systems the results generalize some recent advances due to gauthier and kupka 1992 in continuous time bilinear systems to their discrete time counterparts

a separation principle for bilinear systems with dissipative drift input output stabilization of a class of bilinear systems using a nonlinear stabilizing feedback control law together with an observer is studied in some cases it can be proved that the result is a globally asymptotically stable system

constructive stabilization for quadratic input nonlinear systems in this paper stabilization of nonlinear systems with quadratic multi input is considered with the help of control lyapunov function clf a constructive parameterization of controls that globally asymptotically stabilize the system is proposed two different cases are considered firstly under certain regularity assumptions the feasible control set is parameterized and continuous feedback stabilizing controls are designed then for the general case piecewise continuous stabilizing controls are proposed the design procedure can also be used to verify whether a candidate clf is indeed a clf several illustrative examples are presented as well

a heuristic lagrangean algorithm for the capacitated plant location problem abstract lagrangean techniques have been widely applied to the uncapacitated plant location problem and in some cases they have proven to be successfull even when capacitated problems with additional constraints are taken into account in our paper we study the application of these techniques to the capacitated plant location problem when the model considered is a pure integer one several lagrangean decompositions are considered and for some of them heuristic algorithms have been designed to solve the resulting lagrangean subproblems the heuristics consisting of a two phase procedure the first location phase defines a set of multipliers from the analysis of the dual lp relaxation and makes a choice of the plants considering the resulting subproblems as a particular case of the general assignment problems several heuristics have been studied for this second phase based either on a decomposition of knapsack type subproblems through a definition of a set of penalties or of looking into the duality gap and trying to reduce it computational experience is reported

static output feedback and guaranteed cost control of a class of discrete time nonlinear systems with partial state measurements abstract in this paper both the static output feedback issue and the observer based control of a class of discrete time nonlinear systems are considered thanks to a newly developed linearization lemma it is shown that the solution of the discrete time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint an illustrative example is provided to show the usefulness of the proposed control designs

recursive design of discontinuous controllers for uncertain driftless systems in power chained form investigates the problem of almost asymptotic stabilization for a class of uncertain driftless systems in power chained form the main obstacles for the control of this new type of driftless systems are i nonexistence of any time invariant smooth or even continuous state feedback control law ii lack of affineness in the control input and iii high order nonlinearities that make most of the nonlinear design methods inapplicable to overcome these difficulties we propose a constructive approach that combines a discontinuous change of coordinates and the recent adding a power integrator technique sufficient conditions are given under which discontinuous robust and adaptive controllers can be explicitly constructed achieving almost stabilization and adaptive regulation solutions to the problems of global robust regulation and adaptive regulation are also obtained by using switching control schemes

stability improvement of nonlinear systems by feedback this paper is concerned with the property of stabilizing a nonlinear system to a specified equilibrium point arbitrarily fast by appropriate smooth feedback two closely related forms of this property are explored one refers to the asymptotic transfer to the critical point with exponential decay and it is shown that the systems possessing the above property are precisely those whose corresponding linearization is controllable the second stabilizability form defined here amounts to driving the system back to an arbitrarily small neighborhood of the given point arbitrarily fast by smooth feedback a global stabilization result is also included finding application in hamiltonian systems special emphasis is given to the bilinear case

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

extensions to a lagrangean relaxation approach for the capacitated warehouse location problem abstract in this paper we present a lower bound for the capacitated warehouse location problem based upon the lagrangean relaxation of a mixed integer formulation of the problem where we use subgradient optimisation in an attempt to maximise this lower bound problem reduction tests based upon this lower bound and the original problem are given incorporating this bound and the reduction tests into a tree search procedure enables us to solve problems involving up to 50 warehouses and 150 customers

control of systems without drift via generic loops this paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift it is based on the generation of nonsingular loops which allow linearized controllability along suitable trajectories once such loops are available it is possible to employ standard newton or steepest descent methods as classically done in numerical control the theoretical justification of the approach relies on results establishing the genericity of nonsingular controls as well as a simple convergence lemma

homogeneity with incremental degrees and global stabilisation of a class of high order upper triangular systems the problem of global asymptotic stabilisation is investigated for a class of upper triangular systems with uncontrollable linearisation a notion of generalised homogeneity is introduced in this article providing a new insight and a deeper perspective on how to categorise nonlinear terms into the higher order and equal order terms in a non traditional way the delicate analysis and new categorisation of the vector field make it possible to encompass more general nonlinearities a globally stabilising controller is recursively constructed by a bottom up step by step procedure containing the equal order terms as its indispensable components it is illustrated that the results obtained in this article incorporate and extend existing results for the global stabilisation of upper triangular systems

feedback stabilization of a class of nonsmooth systems in this paper we investigate global stabilization of nonsmooth systems the aim is to provide sufficient condition based on standard derivative for feedback stabilization of nonsmooth systems by means of a feedback of class cr r 1 the main result is a generalization of a result concerning smooth systems see for instance j control optimization 32 1994 358 to systems that are only continuous and locally lipschitz

time varying feedback control of nonaffine nonlinear systems without drift sufficient conditions are presented under which a general nonlinear system without drift is globally asymptotically stabilizable by time varying state feedback a novel approach is developed for the design of a time varying smooth state feedback controller the controller is explicitly constructed by using the bounded state feedback strategy lin 1995 1996 combined with lyapunov technique as well as lossless systems theory this work incorporates earlier global stabilization results coron 1992 pomet 1992 for controllable affine systems without drift which are known not to be smoothly stabilizable via any time invariant state feedback

a dynamic extension for l sub g v controllers a dynamic state feedback control structure is proposed the scheme is conceived as an adaptive controller with the equilibrium in an l sub g v control law as the uncertain parameter which allows the implementation of the controller for systems with unknown equilibrium a new property of l sub g v controllers is given and it is proven that this and other important properties carry on to the proposed scheme a synchronous machine case study shows that the proposed scheme may give better results than the l sub g v controller from which it is derived

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

global asymptotic stabilization of periodic nonlinear systems with stable free dynamics abstract we consider a nonlinear control system with periodic coefficients we study the problem of asymptotic stabilization of the equilibrium x 0 of the closed loop system by state feedback we assume that the free dynamic system possesses a periodic lyapunov function ensuring lyapunov stability of the equilibrium x 0 we have developed a method for constructing a damping control for affine systems with periodic coefficients based on a generalization of weak jurdjevic quinn conditions using an extension of the notion of the commutator to non stationary vector fields using this approach we obtain sufficient conditions for uniform local and global asymptotic stabilization of general nonlinear systems in particular affine control systems with periodic coefficients stabilization results generalize known results for time invariant systems to time varying periodic systems

hybrid adaptive control laws solving a path following problem for non holonomic mobile manipulators in this paper a general solution to the path following problem for mobile manipulators with non holonomic mobile platform has been presented new proposed control algorithms for mobile manipulators with fully known dynamics or with parametric uncertainty in the dynamics take into considerations the kinematics as well as the dynamics of the non holonomic mobile manipulator the convergence of the control algorithms is proved using the lasalle s invariance principle

uniqueness of multiplicative determinants on elliptic pseudodifferential operators we describe all multiplicative determinants on the pathwise connected component of identity in the group of invertible classical pseudodifferential operators on a closed manifold that are continuous along continuous paths and the restriction to zero order operators of which is of class c1 this boils down to a description of all traces on zero order classical pseudodifferential operators which turn out to be linear combinations of the wodzicki residue w and leading symbol traces introduced in pr1 both of which are continuous consequently multiplicative determinants are parametrized by the residue determinant w87 sc and a new leading symbol determinant both of which are expressed in terms of a homogeneous component of the symbol of the logarithm of the operator

control of high order nonholonomic systems in power chained form using discontinuous feedback addresses the problems of almost asymptotic stabilization and global asymptotic regulation gar for a class of high order nonholonomic systems in power chained form this particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years the nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods sufficient conditions are presented under which a discontinuous state feedback control law or a switching controller can be recursively constructed using the so called adding a power integrator technique of c qian et al 2001 we also illustrate how the results can be extend to multi input systems in power chained form simulation examples are provided to demonstrate the effectiveness of the proposed controllers

brief discontinuous exponential stabilization of chained form systems in this paper a novel approach to exponential stabilization of chained form system is proposed provided that the control law fulfills mild assumptions it is shown that a brunovsky like change of coordinates depending on the control transforms any chained form system into a system having a linearly bounded nonlinear part using linear tools it is possible to exponentially stabilize a chained form system for any initial condition outside a submanifold containing the origin this result is then generalized to global exponential stabilization the so obtained static discontinuous feedback is bounded for bounded states and exponentially converges to zero along the closed loop trajectories of the system

passivity and absolute stabilization of a class of discrete time nonlinear systems abstract by using the theory of discrete time passive systems and the concept of feedback equivalence we present an approach toward deriving sufficient conditions for the global stabilization of discrete time nonlinear systems in the form x k 1 tf x k g x k u k the central feature of the approach is that a unifying set of stability criteria can be obtained and the stability results recover the previous stabilization schemes proposed in the literature

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

a passive system approach to feedback stabilization of nonlinear control stochastic systems the purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws in particular we prove that as in the case of stochastic differential systems affine in the control one can compute stabilizing feedback laws provided the unforced stochastic differential system is lyapunov stable in probability and some rank conditions are fulfilled some well known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems

output feedback control of a class of nonlinear systems a nonseparation principle paradigm considers the problem of global stabilization by output feedback for a family of nonlinear systems that are dominated by a triangular system satisfying a linear growth condition the problem has remained unsolved due to the violation of the commonly assumed conditions in the literature using a feedback domination design method which is not based on the separation principle we explicitly construct a linear output compensator making the closed loop system globally exponentially stable

a branch and price algorithm for the capacitated facility location problem the capacitated facility location problem cflp is a well known combinatorial optimization problem with applications in distribution and production planning it consists in selecting plant sites from a finite set of potential sites and in allocating customer demands in such a way as to minimize operating and transportation costs a number of solution approaches based on lagrangean relaxation and subgradient optimization has been proposed for this problem subgradient optimization does not provide a primal fractional optimal solution to the corresponding master problem however in order to compute optimal solutions to large or difficult problem instances by means of a branch and bound procedure information about such a primal fractional solution can be advantageous in this paper a stabilized column generation method is therefore employed in order to solve a corresponding master problem exactly the column generation procedure is then employed within a branch and price algorithm for computing optimal solutions to the cflp computational results are reported for a set of larger and difficult problem instances

linearized control systems and applications to smooth stabilization for a control system dot x f x u the author proves that for generic feedback laws u such that f x u x does not vanish the linearized control systems around the trajectories of dot x f x u x have the same strong accessibility algebra as f applications are given to the smooth stabilization problem

stabilizability of the angular velocity of a rigid body revisited abstract we prove that the jurdjevic quinn techniques for smooth stabilization can be applied to the equation of the angular velocity of a rigid body an explicit polynomial control is given for the symmetric case

tracking control of nonlinear systems with bounded controls and control rates abstract the problem of tracking control of a class of nonlinear systems subject to control and control rate constraints is considered a continuous time predictive control approach is used to derive the nonlinear constrained control law asymptotically stable tracking is ensured in the absence of saturation the control and control rate constraints are guaranteed to be strictly satisfied by the control law an example is given to demonstrate the effectiveness of the method

feedback stabilization of general nonlinear control systems a passive system approach abstract this paper develops sufficient conditions for a general nonlinear control system 1 x f x u to be locally resp globally asymptotically stabilizable via smooth state feedback in particular it is shown that as in the case of affine systems this is possible if the unforced dynamic system of 1 is lyapunov stable and appropriate controllability like rank conditions are satisfied our results incorporate a series of well known stabilization theorems proposed in the literature for affine control systems and extend them to nonaffine nonlinear control systems

brief stabilization of invariant sets for nonlinear non affine systems the problem of the global and local stabilization of invariant sets for general nonlinear controlled systems is considered new state feedback stabilizing controllers and sufficient conditions of asymptotic stability of a goal set with the specified region of attraction are proposed the proofs of the obtained results are based on the detailed analysis of the w limit sets of the closed loop system with the speed gradient or jurdjevic quinn controllers for affinized controlled system two illustrating examples are given

on persistently exciting observers and a non linear separation principle application to the stabilization of a generator we provide a separation principle for a class of non linear time varying systems the only assumption we make on the state feedback control law is that it does not vanish as the states grow unboundedly for the observer we propose a design method based on the assumption that the system is transformable into a form affine in the unmeasured variable and a property of persistency of excitation this assumption covers but is not restricted to the common observability condition that the vector field multiplying the unmeasured variable is separated from zero for all state values our separation principle relies on stability results for cascades systems

inverse optimization an application to the capacitated plant location problem lagrangean techniques have had wide application to the optimization of discrete optimization problems inverse optimization refers to the fact that each time a lagrangean calculation is made for a specific problem with a given resources vector an optimal solution is obtained for a related problem with a suitably adjusted resources vector this property is studied in depth for the capacitated plant location problem and new parametric methods for that problem are suggested computational experience is reported

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

adaptive control of a class of nonaffine systems using neural networks a neural control synthesis method is considered for a class of nonaffine uncertain single input single output siso systems the method eliminates a fixed point assumption and does not assume boundedness on the time derivative of a control effectiveness term one or the other of these assumptions exist in earlier papers on this subject using lyapunov s direct method it is shown that all the signals of the closed loop system are uniformly ultimately bounded and that the tracking error converges to an adjustable neighborhood of the origin simulation with a van der pol equation with nonaffine control terms illustrates the approach

the geometry of loop spaces ii characteristic classes abstract we develop a theory of chern simons classes cs 2 k 1 w h 2 k 1 lm 2 k 1 r on the loop space lm of a riemannian manifold m these classes are associated to a pair of connections on lm whose connection and curvature forms take values in pseudodifferential operators by 19 we use the wodzicki residue of these operators to define and compute the chern simons classes as an application we prove that 1 diff m for the total space m of circle bundles associated to high multiples of a kahler class over integral kahler surfaces

a lagrangean relax and cut approach for the two stage capacitated facility location problem abstract the two stage capacitated facility location problem is to find the optimal locations of depots to serve customers with a given demand the optimal assignment of customers to depots and the optimal product flow from plants to depots in order to solve this problem a lagrangean heuristic is proposed which is based on the relaxation of the capacity constraints the resulting lagrangean subproblem is an uncapacitated facility location problem with an aggregate capacity constraint and can be solved efficiently by branch and bound methods the best bound available from this relaxation is computed by means of a weighted dantzig wolfe decomposition approach feasible solutions are constructed from those of the lagrangean subproblems by applying simple reassignment procedures furthermore the relaxation is strengthened by adding and dualizing valid inequalities which are violated by the fractional primal solution of the dual master program computational results and comparisons with some other bounds and heuristics for this problem are presented

bounded smooth state feedback and a global separation principle for non affine nonlinear systems abstract in this paper we show that a single input nonlinear system z 0 x g 1 x u g l x u l is globally asymptotically stabilizable by arbitrarily small smooth state feedback if unforced dynamics of are lyapunov stable and satisfies appropriate controllability like rank conditions characterized by the lie bracket of vector fields f0 x and g1 x an explicit smooth state feedback control law is constructed this in turn leads to an analytic resp smooth state feedback control law which solves the problem of global stabilization for analytic resp smooth systems x f x u based on these results we then establish a global separation principle for the system with an output finally we briefly discuss how the results can be extended to a multi input system

on relationships among passivity positive realness and dissipativity in linear systems the notions of passivity and positive realness are fundamental concepts in classical control theory but the use of the terms has varied for lti systems these two concepts capture the same essential property of dynamical systems that is a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment this paper summarizes the connection between these two concepts for continuous and discrete time lti systems beyond that relationships are provided between classes of strictly passive systems and classes of positive real systems the more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy based results the frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity after surveying relevant existing results some clarifying results are presented these involve connections between classes of passive systems and finite gain l2l2 stability as well as asymptotic stability additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results this paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts

approximate solutions to large scale capacitated facility location problems this article presents a heuristic algorithm for solving large scale capacitated facility location problems the algorithm consists of solving a single source facility location problem and then solving a minimum cost network problem the single source problem is solved by applying an iterative procedure in which lower bounds on the optimal objective value are generated through lagrangian relaxation techniques upper bounds on the optimal objective value are obtained by modifying the lagrangian solution to restore feasibility the iterative procedure is terminated when the difference between the two bounds is within a prespecified tolerance further improvement of the objective value is attained by subjecting the single source solution to a network optimization code the heuristic algorithm has been tested on over 300 problems derived in one form or another from the kuehn hamburger test problems the testing has also been undertaken on the problems of van roy which were generated using netgen computational results indicate that our approach can be effective in producing near optimal solutions for problems with as many as 1000 customers and 100 potential facility locations most problems converged within 3 percent of the optimal value requiring only a modest amount of computation on an ibm 3090

global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity abstractthe purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics the method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of lyapunov asymptotic stability in probability for stochastic differential equations in particular we prove that a nonlinear stochastic differential system whose unforced dynamics are lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied in this framework we show that a stabilising smooth state feedback law can be designed explicitly a dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis

input saturation and global stabilization of nonlinear systems via state and output feedback for multi input multi output nonlinear systems whose free dynamics are lyapunov stable the author shows how the problem of global stabilization via dynamic output feedback can be solved by using the technique of input saturation the power of this technique is also illustrated by solving the problem of global stabilization via bounded state feedback for affine nonlinear systems with stable unforced dynamics analogous results are established for discrete time nonlinear systems

passivity and disturbance attenuation via output feedback for uncertain nonlinear systems the authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties the problem is approached by means of adaptive output feedback control which does not require any state observer the results obtained extend an earlier result of steinberg and corless 1985 sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback

brief robust stabilization via iterative state steering with an application to chained form systems an approach is presented for the robust stabilization of non linear systems the proposed strategy can be adopted whenever it is possible to compute a control law that steers the state in finite time from any initial condition to a point closer to the desired equilibrium under suitable assumptions such control law can be applied in an iterative fashion obtaining uniform asymptotic stability of the equilibrium point with exponential rate of convergence small non persistent perturbations are rejected while persistent perturbations induce limited errors in order to show the usefulness of the presented theoretical developments the approach is applied to chained form systems and for illustration simulations results are given for the robust stabilization of a unicycle

direct passivity of a class of mimo non linear systems using adaptive feedback in this paper an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi input multi output mimo non linear system with explicit linear parametric uncertainty equivalent to a passive system these results are an extension of those obtained by the authors for the siso case some stability issues associated to the resultant closed loop passive system are also discussed the results obtained are applied to models of dynamical mimo systems to illustrate the controller design methodology

feedback passivation of discrete time systems under communication constraints passivity is a desirable property of a dynamical system because it implies stability and is invariant under negative feedback and parallel interconnections feedback passivation is the process of making a nonpassive system passive through feedback control in this technical note we study the problem of feedback passivation when the controller has limited information about the state of the plant nonlinear plants that are linear in the control inputs are considered the main result of the technical note is a certainty equivalence principle any state feedback controller that ensures closed loop input strict passivity with index mu using the exact state of the plant will also ensure closed loop stochastic quasi passivity using an estimate of the state provided that the infinity norm of the estimation error process is bounded by some function of mu a corollary is that for linear systems although passivity is more strict than stability feedback passivation does not place more constraints on the estimation error and hence does not demand more from the communication channel than mean square stabilization

stabilization of discrete time nonlinear systems by smooth state feedback abstract for a class of nonlinear discrete time systems of the form x k 1 x k g x k u k we investigate conditions under which a nonlinear system can be rendered globally asymptotically stable via smooth state feedback our main result is that any nonlinear system with lyapunov stable unforced dynamics can always be globally stabilized by smooth state feedback if suitable controllability like rank conditions are satisfied several examples are presented to demonstrate the applications of the stability results developed in this paper