finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information this paper studies the problem of finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information the partly usable model information is considered following a certain bernoulli distributed white noise sequence the objective of the study is to design a state feedback controller such that the augmented closed loop system is mean square stochastically finite time bounded and a tracking performance level is achieved over a finite time interval by using the mode dependent diagonally dominant lyapunov function approach some sufficient conditions are established for the existence of an admissible state feedback controller based on these a state feedback controller can be constructed by using a simple matrix decoupling approach two numerical examples and a modified general economic model are presented to demonstrate the effectiveness of our proposed approach

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

partially mode dependent l2 l filtering for discrete time nonhomogeneous markov jump systems with repeated scalar nonlinearities abstract this paper is concerned with the problem of partially mode dependent l 2 l filtering for discrete time nonhomogeneous markov jump systems mjss with repeated scalar nonlinearities our main purpose is to design a partially mode dependent l 2 l filter such that the filtering error system is stochastically stable with l 2 l performance the time varying transition probabilities tps are depicted as a polytope by adopting the diagonally dominant lyapunov functional and based on linear matrix inequalities lmis sufficient conditions are presented for the existence of the filter three examples are given to validate the effectiveness of our results

finite time resilient reliable sampled data control for fuzzy systems with randomly occurring uncertainties abstract this paper deals with the problem of finite time passivity based h resilient reliable state feedback sampled data control for takagi sugeno fuzzy systems with randomly occurring uncertainties and gain variations where the randomly occurring characteristics are designed by stochastic variables satisfying the bernoulli distribution the main objective of this paper is to design a resilient reliable sampled data controller such that the resulting closed loop system is finite time bounded and satisfies finite time mixed h and passive performance index based on the constructed lyapunov krasovskii functional and wirtinger integral inequality some delay dependent sufficient conditions are derived for achieving the required result of the considered systems moreover the derived finite time stability conditions are established in the form of linear matrix inequalities lmis which can be solved by matlab lmi toolbox finally two numerical examples are presented to demonstrate the applicability of the proposed control design technique

two linear transformations each tridiagonal with respect to an eigenbasis of the other let k denote a field and let v denote a vector space over k with finite positive dimension we consider a pair of linear transformations a v v and a v v satisfying both conditions below 1 i there exists a basis for v with respect to which the matrix representing a is diagonal and the matrix representing a is irreducible tridiagonal 2 ii there exists a basis for v with respect to which the matrix representing a is diagonal and the matrix representing a is irreducible tridiagonal we call such a pair a leonard pair on v refining this notion a bit we introduce the concept of a leonard system we give a complete classification of leonard systems integral to our proof is the following result we show that for any leonard pair a a on v there exists a sequence of scalars taken from k such that both 0 a a2a aa a a a2 aa a a a 0 a a 2a a aa aa 2 a a aa a where r s means rs sr the sequence is uniquely determined by the leonard pair if the dimension of v is at least 4 we conclude by showing how leonard systems correspond to q racah and related polynomials from the askey scheme

balanced leonard pairs let k denote a field and let v denote a vector space over k with finite positive dimension by a leonard pair on v we mean an ordered pair of linear transformations a v v and a v v that satisfy the following two conditions i there exists a basis for v with respect to which the matrix representing a is irreducible tridiagonal and the matrix representing a is diagonal ii there exists a basis for v with respect to which the matrix representing a is irreducible tridiagonal and the matrix representing a is diagonal let v0 v1 vd respectively v0 v1 vd denote a basis for v that satisfies i respectively ii for 0 i d let ai denote the coefficient of vi when we write avi as a linear combination of v0 v1 vd and let ai denote the coefficient of vi when we write a vi as a linear combination of v0 v1 vd in this paper we show a0 ad if and only if a0 ad moreover we show that for d 1 the following are equivalent i a0 ad and a1 ad 1 ii a0 ad and a1 ad 1 iii ai ad i and ai ad i for 0 i d these give a proof of a conjecture by the second author we say a a is balanced whenever ai ad i and ai ad i for 0 i d we say a a is essentially bipartite respectively essentially dual bipartite whenever ai respectively ai is independent of i for 0 i d observe that if a a is essentially bipartite or dual bipartite then a a is balanced for d 2 we show that if a a is balanced then a a is essentially bipartite or dual bipartite

robust h control for switched systems with input delays a sojourn probability dependent method in this paper a sojourn probability dependent method is proposed to investigate the robust h control for a class of switched systems with input delays the considered system has the following characteristics 1 it is a switched system consisting of a set of subsystems 2 sojourn probabilities i e the probability of switched systems staying in each subsystem are assumed to be known or partly known a prior and 3 there are input delays and parameter uncertainties in each subsystem by using the sojourn probability information a new type of switched system model is built by using the lyapunov functional method the robust mean square stability criteria are obtained for switched systems under two conditions a all sojourn probabilities of the subsystems are known b only partly sojourn probabilities are known then the robust h controller feedback gains are derived by using the cone complement linearization method an inverted pendulum system and a numerical example are given to demonstrate the effectiveness and applicability of the proposed method

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

h control of 2 d continuous markovian jump delayed systems with partially unknown transition probabilities abstract this study focuses on stochastic stability and h control of two dimensional 2 d continuous delayed markovian jump systems mjss with partial information on transition probability at first a sufficient condition for the stochastic stability of 2 d mjss is proposed by choosing an appropriate lyapunov krasovskii functional then the results are developed by designing a state feedback controller that guarantees the stochastic stability of the resultant closed loop system with a prescribed h performance level finally the proposed results are validated with the help of examples

static output feedback control of nonhomogeneous markovian jump systems with asynchronous time delays this paper investigates the problem of static output feedback control for a class of nonhomogeneous markovian jump system nmjs with asynchronous time delays atds since the atds subject to uncertain transition probabilities tps are taking into account in a practical phenomenon new approaches are introduced to deal with the atds characterized by nonhomogeneous markov processes it is assumed that the communication links are not perfect due to its detrimental effect on the performance of systems stochastic variables are presented to characterize the data transmission which are depending on operation modes and satisfying the bernoulli distribution sets of slack variables are adopted to decouple the product terms between system matrices and lyapunov matrices based on an extended lyapunov function combined with finsler inequality approach the robust static output feedback controller is designed for the closed loop nmjs finally a numerical example is provided to verify the design method

brief paper stabilization of markovian jump linear system over networks with random communication delay this paper is concerned with the stabilization problem for a networked control system with markovian characterization we consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a markov chain the resulting closed loop system is modeled as a markovian jump linear system with two jumping parameters and a necessary and sufficient condition on the existence of stabilizing controllers is established an iterative linear matrix inequality lmi approach is employed to calculate a mode dependent solution finally a numerical example is given to illustrate the effectiveness of the proposed design method

finite time control of discrete time linear systems in this note we consider the finite time stabilization of discrete time linear systems subject to disturbances generated by an exosystem finite time stability can be used in all those applications where large values of the state should not be attained for instance in the presence of saturations the main result provided in the note is a sufficient condition for finite time stabilization via state feedback this result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite time stability all the conditions are then reduced to feasibility problems involving linear matrix inequalities lmis some numerical examples are presented to illustrate the proposed methodology

a unified framework for asymptotic and transient behavior of linear stochastic systems abstract this paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems in order to explain this problem explicitly a concept of mean square stability is first introduced and two stability criteria are derived by utilizing an auxiliary definition of mean square t stability the relations among mean square stability mean square t stability and finite time stochastic stability are established subsequently two new sufficient conditions for the existence of state and output feedback mean square stabilization controllers are presented in terms of matrix inequalities a numerical algorithm is given to obtain the relation between min and finally an example is given to illustrate our results

robust finite time sampled data control of linear systems subject to random occurring delays and its application to four tank system this work studies the problem of robust finite time sampled data control of linear systems subject to random occurring delays and its application to four tank system the input time delays are described by bernoulli distributed white sequences by employing a newly augmented lyapunov krasovskii functional with jensen s inequality free weighting matrix method and wirtinger based double integral inequality approach some less conservative delay dependent conditions for finite time sampled data control law are obtained finally to reveal the proposed technique an application to a four tank system is addressed to illustrate the effectiveness of developed techniques

bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant lyapunov functions or storage functions satisfying appropriate linear matrix inequalities results are also presented for model reduction errors for such systems

nonstationary l2 l filtering for markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities abstract this paper is concerned with nonstationary l 2 l filtering for markov switching repeated scalar nonlinear systems msrsnss with randomly occurring nonlinearities rons where measurement output is modeled by a mode dependent random variable that satisfying bernouli distribution the new relationship are proposed to depict multiple mutually independent markov chains between original mmsrsnss and nonstationary filters by constructing a proper lyapnov function the msrsnss is stochastically stable with l 2 l performance level is guaranteed accordingly the nonstationary filters are designed where filters are characterised by a two layer structure the paper provides a numerical example verifying the efficacy of established technique

on energy to peak filtering for nonuniformly sampled nonlinear systems a markovian jump system approach this paper focuses on the filter design for nonuniformly sampled nonlinear systems which can be approximated by takagi sugeno t s fuzzy systems the sampling periods of the measurements are time varying and the nonuniform observations of the outputs are modeled by a homogenous markov chain a mode dependent estimator with a fast sampling frequency is proposed such that the estimation can track the signal to be estimated with the nonuniformly sampled outputs the nonlinear systems are discretized with the fast sampling period by using an augmentation technique the corresponding stochastic estimation error system is obtained by studying the stochastic stability and the energy to peak performance of the estimation error system we derive the linear matrix inequality based sufficient conditions the parameters of the mode dependent estimator can be calculated by using the proposed iterative algorithm two examples are used to demonstrate the design procedure and the efficacy of the proposed design method

exponential stabilization of a class of stochastic system with markovian jump parameters and mode dependent mixed time delays in this technical note the globally exponential stabilization problem is investigated for a general class of stochastic systems with both markovian jumping parameters and mixed time delays the mixed mode dependent time delays consist of both discrete and distributed delays we aim to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense first by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem then a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality lmi approach finally it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of lmis numerical simulation is carried out to demonstrate the effectiveness of the proposed methods

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

dissipativity based asynchronous filtering for periodic markov jump systems abstract this paper is devoted to developing a periodic and asynchronous filter for periodic markov jump systems a periodic and asynchronous filter means that the filter parameters are s periodic for a given operating mode and its operating modes are unnecessary to be identical but form a periodic hidden markov model together with the modes of the plant a sufficient condition is proposed to guarantee that the filtering error system is exponentially mean square stable and strictly q s r dissipative to realize this filter a slack matrix is introduced to deal with the nonlinearity and finsler s lemma is applied such that the decision variables are reduced finally a numerical simulation provides verification for the effectiveness of our designed filter

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

the end parameters of a leonard pair abstract fix an algebraically closed field f and an integer d 3 let v be a vector space over f with dimension d 1 a leonard pair on v is a pair of diagonalizable linear transformations a v v and a v v each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one there is an object related to a leonard pair called a leonard system it is known that a leonard system is determined up to isomorphism by a sequence of scalars i i 0 d i i 0 d i i 1 d i i 1 d called its parameter array the scalars i i 0 d resp i i 0 d are mutually distinct and the expressions i 2 i 1 i 1 i i 2 i 1 i 1 i are equal and independent of i for 2 i d 1 write this common value as 1 in the present paper we consider the end parameters 0 d 0 d 1 d 1 d of the parameter array we show that a leonard system is determined up to isomorphism by the end parameters and we display a relation between the end parameters and using this relation we show that there are up to isomorphism at most d 1 2 leonard systems that have specified end parameters the upper bound d 1 2 is best possible

fault detection for discrete time markov jump linear systems with partially known transition probabilities in this article the fault detection fd problem for a class of discrete time markov jump linear system mjls with partially known transition probabilities is investigated the proposed systems are more general which relax the traditional assumption in markov jump systems that all the transition probabilities must be completely known a residual generator is constructed and the corresponding fd is formulated as an h filtering problem by which the error between residual and fault are minimised in the h sense the linear matrix inequality based sufficient conditions for the existence of fd filter are derived a numerical example on a multiplier accelerator model economic system is given to illustrate the potential of the developed theoretical results

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

a parallel adaptive finite volume method for nanoscale double gate mosfets simulation we propose in this paper a quantum correction transport model for nanoscale double gate metal oxide semiconductor field effect transistor mosfet device simulation based on adaptive finite volume parallel domain decomposition monotone iterative and a posteriori error estimation methods the model is solved numerically on a pc based linux cluster with mpi libraries quantum mechanical effect plays an important role in semiconductor nanoscale device simulation to model this effect a physical based quantum correction equation is derived and solved with the hydrodynamic transport model numerical calculation of the quantum correction transport model is implemented with the parallel adaptive finite volume method which has recently been proposed by us in deep submicron semiconductor device simulation a 20 nm double gate mosfet is simulated with the developed quantum transport model and computational technique compared with a classical transport model it is found that this model can account for the quantum mechanical effects of the nanoscale double gate mosfet quantitatively various biasing conditions have been verified on the simulated device to demonstrate its accuracy furthermore for the same tested problem the parallel adaptive computation shows very good computational performance in terms of the mesh refinements the parallel speedup the load balancing and the efficiency