h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

a linear matrix inequality approach for robust control of systems with delayed states abstract this paper addresses the robust stabilization problem for uncertain systems with delayed states the parameter uncertainties are unknown but norm bounded and the delay is time varying in this study a linear matrix inequality lmi approach for robust stability analysis for the nominal unforced system and a method for robust stabilization for a class of uncertain delay systems via linear memoryless state feedback control are presented the results depend on the size of the delay and are given in terms of linear matrix inequalities

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

note efficient heuristic algorithms for positive 0 1 polynomial programming problems we develop in this paper two types of heuristic methods for solving the positive 0 1 polynomial programming pp problem of finding a 0 1 vector x that maximizes ctx subject to fx b where c b 0 and f is an m vector of polynomials with non negative coefficients the various heuristics were first tested on randomly generated sparse problems of up to 50 variables and 50 constraints and their performance in terms of computational time and effectiveness was investigated the results were very encouraging optimal solutions were consistently obtained by some of the heuristic methods in over 50 of the problems solved the effectiveness was on the average better than 99 and no less than 96 5 the computational time using these heuristics is on the average 5 of the time required to solve the pp problems to optimality some results for very sparse problems with up to 1 000 variables and 200 constraints are also reported

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

fuzzy controller with stability and performance rules for nonlinear systems this paper presents a fuzzy controller which can be designed through two steps for nonlinear systems the proposed fuzzy controller consists of two groups of fuzzy rules namely the stability and performance rules stability conditions which involve the stability rules only will be derived to guarantee the system stability by properly designing the shapes of the membership functions of the fuzzy controller the stability conditions can be relaxed the proposed fuzzy controller offers a property that the performance rules will not alter the system stability this favorable property enables the performance rules to be designed freely to achieve the system performance without affecting the system stability consequently the system stability and performance can be designed in two separate processes an application example will be presented to show the merits of the proposed approach

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

observer based robust h sub spl infin control for fuzzy systems using two step procedure this paper investigates both robust h sub spl infin analysis and synthesis problems involving observer based fuzzy control via linear matrix inequality methods for which efficient optimization techniques are available the observer and controller are capable of disturbance rejection in the presence of unknown but bounded disturbance we present results in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are demonstrated by examples

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

h sub spl infin control for asymptotically stable nonlinear systems this paper deals with the problem of h sub spl infin control for a class of nonlinear systems the system under consideration is assumed to be globally asymptotically stable with a known lyapunov function based on this lyapunov function and using the notion of dissipativeness a state feedback controller is designed which renders the closed loop system globally asymptotically stable with a prescribed bound on the l sub 2 gain from the disturbance input to the controlled output the proposed controller design method is based on the explicit construction of a lyapunov function for the closed loop system which represents a significant advantage over existing methods

dynamic approximate solutions of the hj inequality and of the hjb equation for input affine nonlinear systems the solution of most nonlinear control problems hinges upon the solvability of partial differential equations or inequalities in particular disturbance attenuation and optimal control problems for nonlinear systems are generally solved exploiting the solution of the so called hamilton jacobi hj inequality and the hamilton jacobi bellman hjb equation respectively an explicit closed form solution of this inequality or equation may however be hard or impossible to find in practical situations herein we introduce a methodology to circumvent this issue for input affine nonlinear systems proposing a dynamic i e time varying approximate solution of the hj inequality and of the hjb equation the construction of which does not require solving any partial differential equation or inequality this is achieved considering the immersion of the underlying nonlinear system into an augmented system defined on an extended state space in which a locally positive definite storage function or value function can be explicitly constructed the result is a methodology to design a dynamic controller to achieve l2 disturbance attenuation or approximate optimality with asymptotic stability

parametric identification of structured nonlinear systems in this paper identification of structured nonlinear systems is considered using linear fractional transformations lft the a priori information regarding the structural interconnection is systematically exploited a parametric approach to the identification problem is investigated where it is assumed that the linear part of the interconnection is given and the input to the nonlinear part is measurable an algorithm for the identification of the nonlinear part is proposed the uniqueness properties of the estimate provided by the algorithm are examined it is shown that the estimate converges asymptotically to its true value under a certain persistence of excitation condition two simulated examples and a real data example are presented to show the effectiveness of the proposed algorithm

robustness analysis and synthesis for nonlinear uncertain systems a state space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed the robustness of a class of nonlinear systems subject to l sub 2 bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality nlmi which yields a convex feasibility problem as in the linear case scalings are used to find a lyapunov or storage function that give sufficient conditions for robust stability and performances sufficient conditions for the solvability of robustness synthesis problems are represented in terms of nlmis as well with the proposed nlmi characterizations it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking lyapunov stability the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes and the computations are reduced to solving linear matrix inequalities unfortunately while the development in this paper parallels the corresponding linear theory the resulting computational consequences are of course not as favourable

an inequality governing nonlinear h control abstract this note gives necessary and sufficient conditions for solving a reasonable version of the nonlinear h control problem the most objectionable hypothesis is elegant and holds in the linear case but every possibly may not be forced for nonlinear systems what we discover in distinction to isidori and astolfi 1992 and ball et al 1993 is that the key formula is not a nonlinear riccati partial differential inequality but a much more complicated inequality mixing partial derivatives and an approximation theoretic construction called the best approximation operator this chebeshev riccati inequality when specialized to the linear case gives the famous solution to the h control problem found in doyle et al 1989 while complicated the chebeshev riccati inequality is modulo a considerable number of hypotheses behind it a solution to the nonlinear h control problem it should serve as a rational basis for discovering new formulas and compromises we follow the conventions of ball et al 1993 and this note adds directly to that paper

d optimal input design for nonlinear fir type systems optimal input design is an important step of the identification process in order to reduce the model variance in this work a d optimal input design method for finite impulse response type nonlinear systems is presented the optimization of the determinant of the fisher information matrix is expressed as a convex optimization problem this problem is then solved using a dispersion based optimization scheme which is easy to implement and converges monotonically to the optimal solution without constraints the optimal design cannot be realized as a time sequence by imposing that the design should lie in the subspace described by a symmetric and non overlapping set a realizable design is found a graph based method is used in order to find a time sequence that realizes this optimal constrained design these methods are illustrated on a numerical example of which the results are thoroughly discussed additionally the computational speed of the algorithm is compared with the general convex optimizer cvx

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

polynomial fuzzy observed state feedback stabilization via homogeneous lyapunov methods a homogeneously state dependent polynomial lyapunov function for an observed state feedback polynomial fuzzy control system is proposed from which an advanced sufficient sum of squares sos condition formulated in terms of state dependent matrix inequalities to achieve fuzzy stabilization is derived three main features compared with existing nonhomogeneously polynomial methods are as follows 1 homogeneous lyapunov function and its time derivative are nicely linked via the hessian matrix 2 removing the nonconvex obstacles on dot p x when deriving a nonhomogeneous lyapunov stabilization condition dot v x 3 separation principle holds since common p falls out as a special case the proposed homogeneous sos approach is placed ahead of the existing sos based methods found in polynomial fuzzy stabilization controls to verify the problem solving theories of the homogeneous polynomial method announced four examples are demonstrated to show the promising features of the approach adduced finally an appendix illustrating the solving procedure is added for clarification on how the examples are solved via sos

polynomial fuzzy models for nonlinear control a taylor series approach classical takagi sugeno t s fuzzy models are formed by convex combinations of linear consequent local models such fuzzy models can be obtained from nonlinear first principle equations by the well known sector nonlinearity modeling technique this paper extends the sector nonlinearity approach to the polynomial case this way generalized polynomial fuzzy models are obtained the new class of models is polynomial both in the membership functions and in the consequent models importantly t s models become a particular case of the proposed technique recent possibilities for stability analysis and controller synthesis are also discussed a set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard t s approaches as the degrees of the involved polynomials increase

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

polynomial fuzzy model based control systems stability analysis via piecewise linear membership functions this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems using the sum of squares sos approach the pfmb control system under consideration requires that the polynomial fuzzy model and polynomial fuzzy controller share neither the same premise membership functions nor the same number of fuzzy rules this class of pfmb control systems offers a greater design flexibility to the polynomial fuzzy controller however due to the imperfectly matched membership functions it usually produces more conservative stability conditions by following the traditional stability analysis approach for the fmb control systems to facilitate the stability analysis piecewise linear membership functions plmfs are proposed which offer a nice property that the grades of membership are governed by a finite number of sample points thus it allows the plmfs to be brought to the sos based stability conditions which are applied to the pfmb control systems with the specified plmfs rather than any shapes the system stability can be examined by checking only the pfmb control system at the sample points it is worth mentioning that the plmfs which are not necessarily implemented physically are a mathematical tool to carry out the stability analysis to verify the stability analysis result a simulation example is given to demonstrate the effectiveness of the proposed approach

relaxed stability and performance lmi conditions for takagi sugeno fuzzy systems with polynomial constraints on membership function shapes most linear matrix inequality lmi fuzzy control results in literature are valid for any membership function i e independent of the actual membership shape hence they are conservative with respect to other nonlinear control approaches when specific knowledge of the shapes is available this paper presents relaxed lmi conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints generalizing previous works by the authors interesting particular cases are overlap product bounds and ellipsoidal regions numerical examples illustrate the achieved improvements as well as the possibilities of solving some multiobjective problems the results also apply to polynomial in membership takagi sugeno fuzzy systems

stability analysis for a class of nonlinear discrete time control systems subject to disturbances and to actuator saturation this paper addresses the stability characterisation problem for a class of nonlinear discrete time control systems subject to actuator saturation and energy bounded disturbance inputs the considered class of systems covers all nonlinear discrete time systems that can be modelled by rational difference equations based on quadratic and piecewise quadratic lyapunov functions conditions based on linear matrix inequalities are proposed to analyse the asymptotic stability internal stability and the l2 input to state stability external stability of the closed loop system the proposed conditions are then incorporated into convex optimisation problems to either maximise an estimate of the region of attraction or a bound on the admissible l2 disturbances and also to obtain an estimate of the system l2 gain for an admissible set of disturbances

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

a robust fault detection filter for polynomial nonlinear systems via sum of squares decompositions abstract a novel diagnostic framework is discussed for fault detection of nonlinear systems whose structure is described by multivariate polynomials the trade off between disturbance rejection and fault sensitivity prescriptions is characterized via algebraic geometry conditions and the unknown input observer design problem is formulated via sum of squares sos technicalities by exploiting the results of the positivstellensatz theorem an adaptive threshold logic is proposed to reduce the generation of false alarms and the diagnostic filter capabilities are illustrated via a numerical example taken from the literature

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

spl hscr sub spl infin control of nonlinear systems a convex characterization the nonlinear spl hscr sub spl infin control problem is considered with an emphasis on developing machinery with promising computational properties the solutions to spl hscr sub spl infin control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems the computational implications for the characterization are discussed

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

an accelerated covering relaxation algorithm for solving 0 1 positive polynomial programs the purpose of this note is to present an accelerated algorithm for solving 0 1 positive polynomial pp problems like our covering relaxation algorithm management science 1979 the accelerated algorithm is a cutting plane method which uses the linear set covering problem as a relaxation for pp however a unique and novel feature of the accelerated algorithm is that it attempts to generate cutting planes from heuristic solutions to the set covering problem whenever possible computational results reveal that this strategy of generating cutting planes has led to a significant reduction in the computational time required to solve a pp problem

quadratic stability analysis of the takagi sugeno fuzzy model the nonlinear dynamic takagi sugeno fuzzy model with offset terms is analyzed as a perturbed linear system a sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model the criterion accepts a convex programming formulation of reduced computational cost compared to the common lyapunov matrix approach parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system application examples on fuzzy models of nonlinear plants advocate the efficiency of the method the examples demonstrate reduced conservatism compared to norm based criteria

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

identification of structured nonlinear systems this paper is concerned with the identification of static nonlinear components in a complex interconnected system these nonlinear components are treated nonparametrically in the sense that no natural parameterization is assumed to be available

a new fuzzy lyapunov function for relaxed stability condition of continuous time takagi sugeno fuzzy systems this paper presents a new fuzzy lyapunov function flf for the stability analysis of continuous time takagi sugeno t s fuzzy systems unlike conventional flfs the proposed one depends not only on the fuzzy weighting functions of the t s fuzzy systems but on their first order time derivatives as well based on the proposed flf a sufficient stability condition is derived in the form of linear matrix inequalities depending on the upper bounds on the second order time derivative of the fuzzy weighting functions as well as the first order ones finally some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature

spl hscr sub spl infin control of nonlinear systems via output feedback controller parameterization the standard state space solutions to the spl hscr sub spl infin control problem for linear time invariant systems are generalized to nonlinear time invariant systems a class of local nonlinear output feedback spl hscr sub spl infin controllers are parameterized as nonlinear fractional transformations on contractive stable nonlinear parameters as in the linear case the spl hscr sub spl infin control problem is solved by its reduction to state feedback and output estimation problems together with a separation argument sufficient conditions for spl hscr sub spl infin control problem to be locally solved are also derived with this machinery

on the generalized local stability and local stabilization conditions for discrete time takagi sugeno fuzzy systems in this paper local stability and local stabilization problems are considered for discrete time nonlinear systems represented by takagi sugeno t s fuzzy systems improved methods to assess the local stability design locally stabilizing control laws and estimate the domain of attraction are developed in terms of single parameter minimization problems subject to linear matrix inequality lmi constraints the improvement is achieved by applying a convergent lmi relaxation technique to prove positivity of homogeneous polynomial parameter dependent matrices of arbitrary degree with variables in the simplex we also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the t s fuzzy systems is bounded and less than one finally several illustrative examples demonstrate the validity and efficiency of the proposed method

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

input design for structured nonlinear system identification this paper is concerned with the input design problem for a class of structured nonlinear models this class contains models described by an interconnection of known linear dynamic systems and unknown static nonlinearities many widely used model structures are included in this class the model class considered naturally accommodates a priori knowledge in terms of signal interconnections under certain structural conditions the identification problem for this model class reduces to standard least squares we treat the input design problem in this situation an expression for the expected estimate variance is derived a method for synthesizing an informative input sequence that minimizes an upper bound on this variance is developed this reduces to a convex optimization problem features of the solution include parameterization of the expected estimate variance by the input distribution and a graph based method for input generation

stability analysis and region of attraction estimation using piecewise polynomial lyapunov functions polynomial fuzzy model approach this paper proposes sum of squares sos methodologies for stability analysis and region of attraction roa estimation for nonlinear systems represented by polynomial fuzzy models via piecewise polynomial lyapunov functions pplfs at first two sos based global stability criteria are proposed by applying maximum type and minimum type pplfs respectively it is known that less conservative results can be obtained by reducing global stability to local stability since it is usually the case for nonlinear systems that the stability cannot be reached globally therefore based on the two types of pplfs two local stability criteria are further proposed with the algorithms that enlarge the estimated roa as much as possible the constraints for checking global and local stability and enlarging the estimated roa are represented in terms of bilinear sos problems hence the path following method is applied to solve the bilinear sos problems in the proposed methodologies finally some examples are provided to illustrate the utility of the proposed methodologies

combining pontryagin s principle and dynamic programming for linear and nonlinear systems to study optimal control and disturbance attenuation problems two prominent and somewhat alternative strategies have emerged in the last century dynamic programming dp and pontryagin s minimum principle pmp the former characterizes the solution by shaping the dynamics in a closed loop a priori unknown via the selection of a feedback input at the price however of the solution to typically daunting partial differential equations the latter instead provides extended dynamics that must be satisfied by the optimal process for which boundary conditions a priori unknown should be determined the results discussed in this article combine the two approaches by matching the corresponding trajectories i e combining the underlying sources of information knowledge of the complete initial condition from dp and of the optimal dynamics from pmp the proposed approach provides insights for linear as well as nonlinear systems in the case of linear systems the derived conditions lead to matrix algebraic equations similar to the classic algebraic riccati equations ares although with coefficients defined as polynomial functions of the input gain matrix with the property that the coefficient of the quadratic term of such equation is sign definite even if the corresponding coefficient of the original are is sign indefinite as it is typically the case in the mathcal h infty control problem this feature is particularly appealing from the computational point of view since it permits the use of standard minimization techniques for convex functions such as the gradient algorithm in the presence of nonlinear dynamics the strategy leads to algebraic equations that allow us to locally construct the optimal feedback by considering the behavior of the closed loop dynamics at a single point in the state space

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

control of rational systems using linear fractional representations and linear matrix inequalities abstract every system of the form x f x u y g x u where f and g are rational functions of the state x and linear functions of the input u possesses a linear fractional representation lfr in this lfr the system is viewed as an lti system connected with a diagonal feedback element linear in the state we devise an algorithm for computing lfrs based on this construction we give sufficient conditions for various properties to hold for the open loop system these include checking whether a given polytope is stable finding a lower bound on the decay rate of trajectories initiating in this polytope computing an upper bound on the l2 gain etc all these conditions are obtained by analyzing the properties of a differential inclusion related to the lfr and given as convex optimization problems over linear matrix inequalities lmis we show how to use this approach for static state feedback synthesis we then generalize the results to dynamic output feedback synthesis in the case when f and g are linear in every state coordinate that is not measured extensions towards a class of nonrational and uncertain nonliner systems are discussed

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

brief paper robust h control of uncertain nonlinear systems this paper discusses the robust l 2 gain performance synthesis problem for a class of uncertain nonlinear systems it is shown that the hamilton jacobi equation approach to robust h performance synthesis can be extended to solve this problem based on a positive definite solution of a hamilton jacobi inequality a sufficient condition is given such that the uncertain nonlinear system is robust and stable and its l 2 gain is less than or equal to a prescribed value using this condition a state feedback law and an output feedback law which ensure robust l 2 gain performance of the closed loop system are derived finally an example is given

robust h sub spl infin control for linear discrete time systems with norm bounded nonlinear uncertainties this paper studies the problem of robust control of a class of uncertain discrete time systems the class of uncertain systems is described by a state space model with linear nominal parts and norm bounded nonlinear uncertainties in the state and output equations the authors address the problem of robust h sub spl infin control in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties it has been shown that instead of the nonlinear uncertain system one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed which is in terms of a riccati inequality

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

convex design control for practical nonlinear systems this paper describes a new control scheme for approximately optimal control aoc of nonlinear systems convex control design convcd the key idea of convcd is to transform the approximate optimal control problem into a convex semi definite programming sdp problem contrary to the majority of existing aoc designs where the problem that is addressed is to provide a control design which approximates the performance of the optimal controller by increasing the controller complexity the proposed approach addresses a different problem given a controller of fixed complexity it provides a control design that renders the controller as close to the optimal as possible and moreover the resulted closed loop system stable two numerical examples are used to show the effectiveness of the method

dynamic generalized controllability and observability functions with applications to model reduction and sensor deployment in this paper we introduce the notion of dynamic generalized controllability and observability functions for nonlinear systems these functions are called dynamic and generalized since they make use of additional states dynamic extension and are such that partial differential inequalities are solved in place of equations the presence of the dynamic extension permits the construction of classes of canonical controllability and observability functions without relying on the solution of any partial differential equation or inequality the effectiveness of the proposed concept is validated by means of two applications the model reduction problem via balancing and the sensor deployment problem in a continuous stirred tank reactor cstr

output stabilization of takagi sugeno fuzzy systems abstract in this paper the output stabilization problem of takagi sugeno fuzzy models is considered first a natural form of observers for such models is given sufficient conditions for their asymptotic convergence are given which are dual to those for the stability of state feedback fuzzy controllers we then show that a state feedback controller and an observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the lyapunov method using positive definite matrices in this sense it is shown that the separation principle holds for takagi sugeno fuzzy systems two design examples are given to illustrate the theory

input design via lmis admitting frequency wise model specifications in confidence regions a framework for reformulating input design problems in prediction error identification as convex optimization problems is presented for linear time invariant single input single output systems this framework unifies and extends existing results on open loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided a wide range of model quality constraints can be handled in particular different frequency by frequency constraints can be used this opens up new applications of input design in areas such as robust control furthermore quality specifications can be imposed on all models in a confidence region thus allowing for statements such as with at least 99 probability the model quality specifications will be satisfied

robust h control for a class of uncertain nonlinear switched systems with average dwell time this paper focuses on the robust h control problem for a class of nonlinear switched systems containing neutral uncertainties with average dwell time adt switching uncertainties are considered to be nonlinearly dependent on state and state derivative and allowed to appear in channels of state control input and disturbance input the robust h control problem of the switched system with stabilisable and unstabilisable subsystems is solvable if the stabilisable and unstabilisable subsystems satisfy certain conditions and admissible switching strategy among them adt and piecewise lyapunov function approaches are applied to achieve the control design a numerical example is provided to illustrate the effectiveness of the proposed approach

nonlinear l 2 gain suboptimal control abstract a method of solving the nonlinear local l2 gain suboptimal control problem based on the chain scattering approach is proposed this problem requires the l2 gain of the closed loop to be less than one and closed loop internal stability defined in the small signal input output sense we obtained sufficient conditions for the existence of a suboptimal controller in terms of a state space description of the plant as well as a local state space parameterization of a class of controllers solving the local l2 gain suboptimal problem the design procedure is demonstrated with a numerical example 1997 elsevier science ltd

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal control for polynomial systems using matrix sum of squares relaxations this note deals with a computational approach to an optimal control problem for input affine polynomial systems based on a state dependent linear matrix inequality sdlmi from the hamilton jacobi inequality the design follows a two step procedure to obtain an upper bound on the optimal value and a state feedback law in the first step a direct usage of the matrix sum of squares relaxations and semidefinite programming gives a feasible solution to the sdlmi in the second step two kinds of polynomial annihilators decrease the conservativeness of the first design the note also deals with a control oriented structural reduction method to reduce the computational effort numerical examples illustrate the resulting design method

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

stability analysis of polynomial fuzzy models via polynomial fuzzy lyapunov functions in this paper the stability of continuous time polynomial fuzzy models by means of a polynomial generalization of fuzzy lyapunov functions is studied fuzzy lyapunov functions have been fruitfully used in the literature for local analysis of takagi sugeno models a particular class of the polynomial fuzzy ones based on a recent taylor series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space it is shown that a refinement of the polynomial lyapunov function so as to make it share the fuzzy structure of the model proves advantageous conditions thus obtained are tested via available sos software

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller