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We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high [...]

We consider the use of importance sampling to compute expectations of functionals of Markov processes. For a class of expectations that can be characterized as positive solutions to a linear [...]

We study the long-term behavior of the optimal harvesting policies for a mixed forest composed by multiple species of different maturity ages. This model is a prototype for the exploitation [...]

Motivated by the study of a class of networked control systems, this correspondence paper is concerned with the design problem of stabilization controllers for linear systems with stochastic input delays. Different from the common assumptions on time delays, it is assumed here that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delays, criteria for the stochastic stability and stabilization controller design are derived. Traditionally, in the case that the variation range of the time delay is available, the maximum allowable bound of time delays can be calculated to ensure the stability of the time-delay system. It is shown, via numerical examples, that such a maximum allowable bound could be made larger in the case that the probability distribution of the time delay is known. Index Terms--Delay, linear matrix inequality (LMI), Lyapunov functional, networked control system (NCS), stabilization.

This correspondence paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi-Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this correspondence paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach. Index Terms--Guaranteed cost control, polynomial fuzzy control system, polynomial Lyapunov function, stability, sum of squares (SOS).

In this paper, we are concerned with the problem of stability analysis and stabilization control design for Takagi-Sugeno (T-S) fuzzy systems with probabilistic interval delay. By employing the information of probability distribution of the time delay, the original system is transformed into a T-S fuzzy model with stochastic parameter matrices. Based on the new type of T-S fuzzy model, the delay-distribution-dependent criteria for the mean-square exponential stability of the considered systems are derived by using the Lyapunov-Krasovskii functional method, parallel distributed compensation approach, and the convexity of some matrix equations. The solvability of the derived criteria depends not only on the size of the delay but also on the probability distribution of the delay taking values in some intervals. The revisions of the main criteria in this paper can also be used to deal with the case when only the information of variation range of the delay is considered. It is shown by practical examples that our method can lead to very less conservative results than those by other existing methods. Index Terms--Delay distribution dependent, linear matrix inequality (LMI), Lyapunov-Krasovskii functional, probability distribution, Takagi-Sugeno (T-S) fuzzy model.

This paper presents a unified treatment of the motion control of underactuated two-link manipulators, including acrobots and pendubots. The motion space is divided into two areas: swing-up and attractive; and control laws are designed for each. First, a control law based on a weak-control Lyapunov function (WCLF) is employed to increase the energy of and control the posture of the actuated link in the swing-up area. Next, one parameter of the WCLF is chosen to be a nonlinear function of the state to avoid singularities. Then, another parameter of the control law is adjusted based on the state to improve the control performance. Finally, an optimal control law is designed for the attractive area. Stability is guaranteed in the swing-up area by the use of a WCLF based on LaSalle's invariance principle. Moreover, the global stability of the control system is guaranteed by integrating the WCLF and a nonsmooth Lyapunov function. Index Terms--Acrobot, LaSalle's invariance principle, nonsmooth Lyapunov function (NSLF), singularity, stabilization, underactuated manipulator, weak-control Lyapunov function (WCLF).

This paper presents a new approach for the global robust stabilizing control of a class of dynamic neural network systems. This approach is developed via Lyapunov stability and inverse optimality, which circumvents the task of solving a Hamilton-Jacobi-Isaacs equation. The primary contribution of this paper is the development of a nonlinear [H.sub.[infinity]] control design for a class of dynamic neural network systems, which are usually used in the modeling and control of nonlinear affine systems with unknown nonlinearities. The proposed [H.sub.[infinity]] control design achieves global inverse optimality with respect to some meaningful cost functional, global disturbance attenuation, and global asymptotic stability provided that no disturbance occurs. Finally, four numerical examples are used to demonstrate the effectiveness of the proposed approach. Index Terms--Dynamic neural network system, Hamilton-Jacobi-Isaacs (HJI) equation, inverse optimality, Lyapunov stability, nonlinear [H.sub.[infinity]] control.

In this technical note, the problem of finite time stabilization of linear time-varying continuous systems is considered. Necessary and sufficient conditions, based upon the solution to some Lyapunov differential matrix equations, are proposed for particular cases of interest. From these conditions, the design of time-varying state feedback controller guaranteeing the finite time closed-loop stability is presented. Numerical experiments illustrate the potentialities of the approach. Index Terms--Finite-time stability and stabilization, linear time-varying systems, Lyapunov differential equations, Lyapunov stability.

This paper introduces a novel complex network model to evaluate the reputation of virtual organizations. By using the Lyapunov function and linear matrix inequality approaches, the local synchronization of the proposed model is further investigated. Here, the local synchronization is defined by the inner synchronization within a group which does not mean the synchronization between different groups. Moreover, several sufficient conditions are derived to ensure the local synchronization of the proposed network model. Finally, several representative examples are given to show the effectiveness of the proposed methods and theories. Index Terms--Complex network, linear matrix inequality, local synchronization, Lyapunov functional, reputation computation, trust, virtual organization.

We construct strict Lyapunov functions for broad classes of nonlinear systems satisfying Matrosov type conditions. Our new constructions are simpler than the designs available in the literature. We illustrate the practical interest of our designs using a globally asymptotically stable biological model. Index Terms--Biological systems, Lyapunov function, Matrosov theorem.

This paper develops a Lyapunov approach for studying convergence and stability of a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs describe the dynamics of a general system evolving in a compact convex subset of the state space. In particular, they include the dynamics of the full-range (FR) model of cellular neural networks (CNNs), which is characterized by hard-limiter nonlinearities with vertical segments in the i--v characteristic. The approach is based on the following two main tools: 1) a set-valued derivative, which enables to compute the evolution of a Lyapunov function along the solutions of the DVIs without involving integrations, and 2) an extended version of LaSalle's invariance principle, which permits to study the limiting behavior of the solutions with respect to the invariant sets of the DVIs. Then, this paper establishes conditions for convergence (complete stability) of DVIs in the presence of multiple equilibrium points (EPs), global asymptotic stability (GAS), and global exponential stability (GES) of the unique EP. These conditions are applied to investigate convergence, GAS, and GES for FR-CNNs and some extended classes of FR-CNNs. It is shown that, by means of the techniques developed in this paper, the analysis of convergence and stability of FR-CNNs is no more difficult than that of the standard (S)-CNNs. In addition, there are significant cases, such as the symmetric FR-CNNs and the nonsymmetric FR-CNNs with a Lyapunov diagonally stable matrix, where the proof of convergence or global stability is much simpler than that of the S-CNNs. Index Terms--Cellular neural networks (CNNs), convergence, differential variational inequalities (DVIs), full-range (FR) model, LaSalle's invariance principle, set-valued derivative.

This technical note proposes a novel frequency-selective Kalman-Yakubovich-Popov (FS--KYP) lemma for analysis of single-input single-output (SISO) continuous systems. In contrast to existing approaches, the proposed method only uses a minimal number of variables due to the absence of Lyapunov variables in semidefinite programming (SDP) formulation. The SDP formulation is extended to polytopic uncertain systems also without any additional variable and yields an efficient method for computation of the [H.sub.[infinity]] gain for polytopic systems. The viability of the proposed method are demonstrated through several numerical examples. Index Terms--Kalman--Yakubovich--Popov (KYP) lemma, semi-definite programming (SDP), semi-infinite program (SIP), single-input single-output (SISO).

Recently, we introduced an adaptive control design for linearly parameterized multi-input nonlinear systems admitting a known Control Lyapunov Function (CLF) that depends on the unknown system parameters. The main advantage of that design is that it overcomes the problem where the estimation model becomes uncontrollable (at regions of the state space where the actual system is controllable). However, the resulted adaptive control design is quite complicated and, moreover, it exhibited poor transient behavior in various applications. In this technical note, we propose and analyze a new computationally efficient adaptive control design that overcomes the aforementioned shortcomings. The proposed design is based on an adaptive optimization algorithm introduced recently by the author, which makes sure that the parameters to be optimized (which correspond to the controller parameters in this technical note) are modified so as to both lead to a decrease of the function to be minimized and satisfy a persistence of excitation condition. The main advantage of the proposed adaptive control design is that it can produce arbitrarily good transient performance outside (a) the regions of the state space where the actual system becomes uncontrollable and (b) a region of the parameter estimates space which shrinks exponentially fast. It is also worth noting that the class of systems where the proposed algorithm is applicable is more general than that of our previous work; however, it has to be emphasized that, due to the fact that the proposed algorithm involves the use of random sequences, all the established stability and convergence results are guaranteed to hold with probability one. Index Terms--Adaptive optimization, control Lyapunov functions, multivariable adaptive control, persistence of excitation.

This paper investigates stabilization of switched systems by using a Lyapunov function composed of a family of continuously differentiable functions. Switching laws are constructed by using the directional derivatives along the trajectories of the subsystems. Conditions for stabilization are established with careful consideration of sliding modes and directional derivatives along sliding modes. Three types of composite quadratic Lyapunov functions, the max of quadratics, the min of quadratics and the convex hull of quadratics are used for deriving matrix conditions of stabilization and for constructing switching laws. Dual stabilization results are established with respect to the pair of conjugate Lyapunov functions: the max of quadratics and the convex hull of quadratics. Conditions of stabilization are derived as bilinear matrix inequalities and solved with LMI-based numerical tools. Relationship between the newly derived conditions and some existing conditions are investigated. It is observed that the min of quadratics, which is nondifferentiable and nonconvex, may be a more convenient tool than the other two types of functions which are convex and/or differentiable. Numerical examples are used to demonstrate the synthesis results and the advantage of the composite quadratic functions over existing multiple Lyapunov functions. In particular, better results have been obtained when the number of quadratic functions is greater than the number of subsystems. Index Terms--Bilinear matrix inequality (BMI), composite quadratic functions, sliding mode, stabilization, switched system.

An adaptive interconnected observer and high-order sliding-mode control of induction motors without mechanical sensors (speed sensor and load torque sensor) are proposed and experimentally evaluated. The adaptive interconnected observer estimates fluxes, angular velocity, load torque, and stator resistance. Stability based on Lyapunov theory is proved to guarantee the 'observer-controller' stability. Index Terms--High-order sliding mode (HOSM), induction motor (IM), observer, sensorless control.

A novel method is proposed to obtain the optimum configuration of dynamic vibration absorber (i.e., DVA) attached to an undamped or damped primary structure. The performance index, i.e., the quadratic integration, includes two types of controls, i.e., velocity and displacement controls of the primary mass. Based on the Lyapunov equation, the performance indices are simplified into matrix quadratic forms. With the help of the Kronecker product and matrix column expansion, the closed-form solutions of optimum parameters for undamped primary structure are finally presented. Moreover, in some cases, the method can produce perturbation solutions in simple forms for damped primary, structure. Especially, from these solutions, the classical optimum [H.sub.2] designs under external force or base acceleration excitation can be derived out. [DOI: 10.1115/1.2948373]

In this paper, a synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays. The complex networks addressed which include neural and social networks as special cases are quite general. Rather than the commonly used Lipschitz-type function, a more general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. The distributed infinite time delays in the discrete-time domain are first defined. By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed discrete-time complex network with distributed delays is synchronized if certain linear matrix inequalities (LMIs) are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, for all admissible discrete and distributed delays, the dynamics of the estimation error is guaranteed to be globally asymptotically stable. Again, an LMI approach is developed for the state estimation problem. Two simulation examples are provided to show the usefulness of the proposed global synchronization and state estimation conditions. It is worth pointing out that our main results are valid even if the nominal subsystems within the network are unstable. Index Terms--Complex networks, discrete time delays, distributed time delays, linear matrix inequality (LMI), Lyapunov-Krasovskii functional, neural networks, state estimation, synchronization.

In this paper, the synchronization control problem is considered for two coupled discrete-time complex networks with time delays. The network under investigation is quite general to reflect the reality, where the state delays are allowed to be time varying with given lower and upper bounds, and the stochastic disturbances are assumed to be Brownian motions that affect not only the network coupling but also the overall networks. By utilizing the Lyapunov functional method combined with linear matrix inequality (LMI) techniques, we obtain several sufficient delay-dependent conditions that ensure the coupled networks to be globally exponentially synchronized in the mean square. A control law is designed to synchronize the addressed coupled complex networks in terms of certain LMIs that can be readily solved using the Matlab LMI toolbox. Two numerical examples are presented to show the validity of our theoretical analysis results. Index Terms--Control law, coupled networks, linear matrix inequality (LMI), Lyapunov functional, stochastic disturbance, synchronization, time-varying delay.

The application of Lyapunov's criterion for the asymptotic stability of equilibrium in mechanical systems is difficult in general because the natural candidate for the role of Lyapunov function, the mechanical energy, is suitable for determining simple stability but not asymptotic stability, unless the energy is modified in a way that is nontrivial, difficult to standardize, and whose physical interpretation is obscure. A simple class of mechanical systems is discussed for which the global asymptotic stability can be checked by means of simple physically reasonable Lyapunov functions. A comparison of alternative Lyapunov functions is also done when possible. The class of systems includes the motion of a heavy body moving through the atmosphere close to the Earth's surface. [DOI: 10.1119/1.2897289]

This article is concerned with the efficient numerical solution of the Lyapunov equation [A.sup.T]X + XA = -C with a stable matrix A and a symmetric positive semidefinite matrix C of possibly small rank. We discuss the efficient implementation of Hammarling's method and propose among other algorithmic improvements a block variant, which is demonstrated to perform significantly better than existing implementations. An extension to the discrete-time Lyapunov equation [A.sup.T]XA - X = -C is also described. Categories and Subject Descriptors: F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems--Computations on matrices; G.1.3 [Numerical Analysis]: Numerical Linear Algebra Linear systems (direct and iterative methods) General Terms: Algorithms, Performance Additional Key Words and Phrases: Lyapunov equation, numerical solution, block algorithm ACM Reference Format: Kressner, D. 2008. Block variants of Hammarling's method for solving Lyapunov equations. ACM Trans. Math. Softw. 34, 1, Article 1 (January 2008), 15 pages. DOI = 10.1145/1322436.1322437 http://doi.acm.org/10.1145/1322436.1322437

The insertion of data network in the feedback adaptive control loops makes the analysis and design of networked control systems more complex than traditional control systems. This paper addresses the adaptive stabilization problem of linear time-invariant networked control systems when the measurements of the plant states are corrupted by bounded disturbances. The case of state feedback is treated in which only an upper bound on the norm of matrix A is needed. The problem is to find an upper bound on the transmission period h that guarantees the stability of the overall adaptive networked control system under an ideal transmission process, i.e. no transmission delay or packet dropout. Rigorous mathematical proofs are established, that relies heavily on Lyapunov's stability criterion and dead-zone Technique. Simulation results are given to illustrate the efficacy of our design approach. Keywords: Networked control systems, Transmission period, Dead-zone, Lyapunov's stability, INTRODUCTION In recent years, the discipline of networked control systems has become a highly active research field. An NCS is a control system in which a data network is used [...]

In this note, the problem of Ha filtering for a class of discrete-time switched systems with state delays is investigated. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the [H.sub.[infinity]] sense. By using switched Lyapunov functionals, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs), by solving which a desired [H.sub.[infinity]] filter can be constructed. A numerical example is provided to demonstrate the effectiveness of the proposed techniques. Index Terms--Discrete-time switched system, [H.sub.[infinity]] filter, linear matrix inequality (LMI), switched Lyapunov functional.

This brief addresses the global asymptotic stability (GAS) of delayed neural networks. Based on the Lyapunov method, using some existing results for the existence and uniqueness of the equilibrium point, some sufficient conditions are obtained for checking the GAS without demanding the boundedness and differentiability hypotheses for activation functions. Through comparison, it is illustrated that our conditions extend and improve some recent results. Index Terms--Delayed neural networks, equilibrium point, global asymptotic stability (GAS), Lyapunov functional.

This brief presents a very low complexity hardware interleaver implementation for turbo code in wideband CDMA (W-CDMA) systems. Algorithmic transformations are extensively exploited to reduce the computation complexity and latency. Novel VLSI architectures are developed. The hardware implementation results show that an entire turbo interleave pattern generation unit consumes only 4 k gates, which is an order of magnitude smaller than conventional designs. Index Terms--CDMA, interleaver, turbo codes, VLSI architecture.

In this note, we study the extension of the class of linear time invariant plants that may be transformed into SPR systems introducing an observer. It is shown that for open loop stable systems a cascaded observer achieves the result. For open loop unstable systems an observer-based feedback is required to succeed. In general any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples. Index Terms--Kalman-Yakubovich-Popov (KYP) lemma, Lyapunov functions, observers, passivity, strictly positive realness (SPR), strictly positive realness (SPR) systems.

In this paper, it is shown how standard iterative methods for solving linear and nonlinear equations can be designed from the point of view of control. Appropriate choices of control Lyapunov functions (CLFs) lead to both continuous and discrete-time versions of the Newton-Raphson and conjugate gradient algorithms as well as new variants. Index Terms--Conjugate gradient (CG) algorithm, control Lyapunov functions (CLFs), iterative methods, proportional-integral-derivative control, zero finding methods.

This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode de-de converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs). Index Terms--dc-dc converter, Lyapunov methods, pulsewidth modulated (PWM) systems, sampled data modeling, stability analysis.

In this paper, two new relaxed stabilization criteria for discrete-time T-S fuzzy systems are proposed. In the beginning, the operation state space is divided into several subregions, and then, the T-S fuzzy system is transformed to an equivalent switching fuzzy system corresponding to each subregion. Consequently, based on the piecewise Lyapunov function, the stabilization criteria of the switching fuzzy system are derived. The criteria have two features: 1) the behavior of the two successive states of the system is considered in the inequalities and 2) the interactions among the fuzzy subsystems in each subregion [S.sub.j] are presented by one matrix [X.sub.j]. Due to the above two features, the feasible solutions of the inequalities in the criteria are much easier to be found. In other words, the criteria are much more relaxed than the existing criteria proposed in other literature. The proposed conditions in the criteria and the fuzzy control design can be solved and achieved by means of linear matrix inequality tools. Two examples are given to present the superiority of the proposed criteria and the effectiveness of the fuzzy controller's design, respectively. Index Terms--Fuzzy control, linear matrix inequalities (LMIs), piecewise Lyapunov function, stabilization, switching fuzzy system.

A hybrid control system, integrating principal and compensation controllers, is developed for multiple-input-multiple-output (MIMO) uncertain nonlinear systems. This hybrid control system is based on sliding-mode technique and uses a recurrent cerebellar model articulation controller (RCMAC) as an uncertainty observer. The principal controller containing an RCMAC uncertainty observer is the main controller, and the compensation controller is a compensator for the approximation error of the system uncertainty. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. The Taylor linearization technique is employed to increase the learning ability of RCMAC and the adaptive laws of the control system are derived based on Lyapunov stability theorem and Barbalat's lemma so that the asymptotical stability of the system can be guaranteed. Finally, the proposed design method is applied to control a biped robot. Simulation results demonstrate the effectiveness of the proposed control scheme for the MIMO uncertain nonlinear system. Index Terms--Biped robot, multiple-input--multiple-output (MIMO), nonlinear systems, recurrent cerebellar model articulation controller (RCMAC), sliding-mode control (SMC).

This brief studies uncertain discrete impulsive systems. The robustly asymptotical stability criteria are established for linear discrete impulsive system and a class of uncertain nonlinear discrete impulsive systems, respectively. These stability criteria are expressed in terms of fairly simple algebraic conditions so that they are easy to be tested. Some examples are given to illustrate results obtained by us. Index Terms--Discrete impulsive system, Lyapunov function, robustly asymptotical stability, uncertainty.

This note continues on the results proposed in two previous papers for computing vector 1- or [infinity]-norm based Lyapunov functions for linear discrete-time systems by presenting a finitely terminating algorithm for the construction of Lyapunov functions of that class. The algorithm utilizes the solution of a finite sequence of feasibility linear programs (LPs) with very few constraints or, equivalently, very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved. Index Terms--1-norm, [infinity]-norm, discrete-time system, linear system, Lyapunov function, Lyapunov stability, model predictive control (MPC) stability, vector norm.

The nonstationary and chaotic dynamics of a gyrotron with a nonfixed field structure and the mechanism of transition to self-modulation and chaotic oscillations are analyzed. The dimensions of chaotic attractors are estimated from the Kaplan-Yorke formula and is found to be anomalously high.

We propose a global high-gain scaling-based state-feedback controller for a general class of nonlinear systems containing uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high gain scaling involving appropriate powers of a high gain scaling parameter which is a dynamic signal driven by the state. The design is applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) systems, and also to nontriangular systems as long as a set of linear inequalities involving powers of the polynomial bounds on the ratios of uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov inequalities. Index Terms--Feedforward systems, high gain, nonlinear systems, scaling, strict-feedback systems.

An important problem in the distributed control of large-scale and infinite dimensional systems is related to the choice of the appropriate controller architecture. We utilize backstepping as a tool for distributed control of nonlinear infinite dimensional systems on lattices, and provide the answer to the following question: what is the controller architecture induced by distributed backstepping design? In particular, we study the case in which we start backstepping design with decentralized control Lyapunov function (CLF), and cancel all interactions at each step of backstepping. For this control law we quantify the number of control induced interactions necessary to guarantee desired dynamical behavior of the infinite dimensional system. We also demonstrate how the controllers with favorable architectures can be designed. Index Terms--Controller architecture, distributed backstepping design, systems on lattices.

We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalized with Riemann invariants. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with an hydraulic application, namely the level and flow regulation in an horizontal open channel. Index Terms--Boundary control, conservation laws, hyperbolic systems, Lyapunov function, partial differential equations.

In this brief, we propose a method of synthesizing a model predictive control (MPC) law for linear parameter varying systems. The proposed method is derived by using the parameter dependent Lyapunov function. The proposed MPC algorithm is reduced to the linear matrix inequality problem. It is shown that the proposed control method achieves less conservative results as compared with the several existing methods. A numerical example is provided to illustrate effectiveness of the proposed method. Index Terms--Linear matrix inequality (LMI), linear parameter varying (LPV) system, model predictive control (MPC), parameter dependent Lyapunov function (PDLF).