LMI Approach Research Articles

LMI Approach to Output Feedback Stabilization for Fuzzy Systems with Immeasurable Premise Variables

This paper is concerned with output feedback control design for a fuzzy system with immeasurable premise variables. It is well known that Takagi-Sugeno fuzzy model describes a wide class of nonlinear systems especially when its premise variables include immeasurable functions. However, when it comes to control design of such a fuzzy system with immeasurable premise variables, a conventional parallel distributed compensator (PDC) is not feasible because it shares the same premise variables as those of a fuzzy system. In this paper, we introduce an output feedback controller with the estimate of the premise variables of an original fuzzy system. We then formulate the stabilization problem for a fuzzy system with immeasurable premise variables. Our control design method is based on a set of strict LMI conditions. No tuning parameter is necessary a priori to solve LMI conditions. Our method includes tuning matrices for control gains in a controller and hence they can be chosen to optimize the control performance of the system. Numerical examples are finally given to illustrate our control design method.

Robust H<SUB align=right>∞ control for uncertain delta system with time delays and non-linear perturbations based on delta operators approach

This paper is concerned with the problem of robust control for uncertain delta system with time delays and non-linear perturbations based on delta operators approach. By employing Lyapunov function in delta domain as well as a unified LMI approach, a delay-dependent robust stability criterion is presented. At the same time, the explicit expression of the desired state feedback controller is also given. Furthermore, the criterion can be changed to a traditional discrete result or a continuous one when the sampling period is chosen as 1 or 0. A numerical example illustrates the effectiveness of the method in this paper.

Controller Synthesis for Reusable Agents of Consensus Networks

We consider consensus problem over networks where each agent is modeled as a class of LTI systems. The objective is to make certain output of each agent converge to the (weighted) average of their initial conditions. To solve this consensus problem, we equip each plant with a local dynamic output-feedback controller. The system configuration allows us to decompose the networked system into subsystems characterized by the eigenvalues of Laplacian associated with the network topology. Having recognized that all the eigenvalues of Laplacian are bounded in a circle region, we cast each eigenvalue as an norm bounded uncertainty and use the robust control framework to evaluate the stability of each subsystem. We derive the sufficient condition to ensure that only the zero eigenvalue of Laplacian can touch the boundary of the circle. Based on that condition, we develop sufficient conditions to guarantee the marginal stability of the overall system, which allows us to use LMI approach to synthesize the controller and establish the convergence property of the system. Fianlly, we adopt a two-degree of freedom controller to improve the performance of the system as well as save the controller output energy.

Robust HFormula state feedback control of discrete-time systems with state delay: an LMI approach

Robust HFormula state feedback control of discrete-time systems with state delay: an LMI approach

An intelligent maximum power extraction algorithm for hybrid wind–diesel-storage system

This paper focuses on the development of maximum wind power extraction algorithms for variable speed wind turbines in hybrid wind–diesel storage system (HWDSS). The propose algorithm utilizes Takagi–Sugeno (T–S) fuzzy controller. This algorithm combines the merits of: (i) the capability for dealing with nonlinear systems; (ii) the powerful LMI approach to obtain control gains; (iii) the high performance of integral controller. The algorithm maximizes the power coefficient for a fixed pitch and suddenly load changes. Moreover, it reduces the voltage ripple and stabilizes the system over a wide range of wind speed variations. The control scheme is tested for different real profiles of wind speed pattern and provides satisfactory results.

Robust stability of stochastic Cohen–Grossberg neural networks with mixed time-varying delays

In the paper, the problem of robust exponential stability analysis is investigated for stochastic Cohen–Grossberg neural networks with both interval time-varying and distributed time-varying delays. By employing an augmented Lyapunov–Krasovskii functional, together with the LMI approach and definition on convex set, two delay-dependent conditions guaranteeing the robust exponential stability (in the mean square sense) of addressed system are presented. Additionally, the activation functions are of more general descriptions and the derivative of time-varying delay being less than 1 is released, which generalize and further improve those earlier methods. Numerical examples are provided to demonstrate the effectiveness of proposed stability conditions.

Robust H-infinity estimation for linear time-delay systems: An improved LMI approach

The problem of robust H ∞ estimation for the polytopic uncertain linear system with state delay is considered. Firstly, by introducing two auxiliary matrices a new LMI representation of H ∞ performance is presented for the linear systems with a single time-varying state delay. The proposed criterion exhibits a kind of separation between the system matrices and the positive definite Lyapunov matrices. So the vertex-dependent Lyapunov functions can be adopted, and thus a less conservative result is expected to be obtained.

Robust [formula omitted] filter design for uncertain fuzzy neutral systems

This paper investigates the problem of robust H ∞ filtering for a class of uncertain Takagi–Sugeno (T–S) fuzzy neutral systems with time-varying delay and linear fractional parametric uncertainties. The aim is to design an asymptotically stable fuzzy filter ensuring asymptotical stability and prescribed H ∞ performance of the filtering error system for all admissible uncertainties. Based on the Lyapunov–Krasovskii functional, the Barbalat lemma and the LMI approach, delay-dependent sufficient conditions for the solvability of this problem are proposed in terms of LMIs, and an explicit expression of the desired H ∞ fuzzy filter is readily given when these LMIs are feasible. Finally, the H ∞ filter design problem for a neutral-type nonlinear distributed network (long line with tunnel diode) is considered in the simulation example to demonstrate the effectiveness and applicability of the proposed method.

Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach

This paper focuses on the problem of global exponential stability analysis of impulsive neural networks with variable delay. Three types of impulses are considered: the impulses are input disturbances; the impulses are ldquoneutralrdquo type (that is, they are neither helpful for stability of neural networks nor destabilizing); and the impulses are stabilizing. For each type of impulses, by using Lyapunov function and Razumikhin-type techniques, the sufficient conditions for global exponential stability are developed in terms of linear matrix inequalities with respect to suitable classes of impulse time sequences. The new sufficient stability conditions do not impose any restriction on the size of time-delay. Numerical examples are given which show our results are less conservative than the existing sufficient stability conditions.

Reliable H ∞ control of a class of uncertain interconnected systems: an LMI approach

The aim of this work is to study the reliable control design problem for parameter-dependent interconnected systems in the presence of actuator failures. Moreover, the control ensures H ∞ performance in front of L 2 perturbations. A more practical model of actuators or control channel failures than outage is adopted, considering partial achievement. The continuous H∞ control problem is solved via elementary manipulations on linear matrix inequalities and the resulting control systems are robustly stable against plant uncertainties and failures.

Comment on “Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic: An LMI approach” by V. Singh [Digital Signal Process. 16 (2006) 45–51

A recently reported criterion for the elimination of overflow oscillations in fixed-point state-space digital filters employing saturation arithmetic is reviewed. It is shown that this criterion is not new and can be obtained directly from a previously reported criterion as a special case.

Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach

This paper investigates the stability and stabilization problem of fractional-order linear systems with nonlinear uncertain parameters, which allow second-order uncertain parameters. The uncertainty in the fractional-order model appears in the form of a combination of additive uncertainty and multiplicative uncertainty. It is shown that the fractional-order model has a strong practical background. Sufficient conditions for the stability and stabilization of such fractional-order model are presented in terms of linear matrix inequalities. Two examples are given to show the effectiveness of the proposed results.

Decentralized Stabilization of Uncertain Systems With Interconnection and Feedback Delays: An LMI Approach

This note presents a broad LMI condition that can ascertain the stability of uncertain systems under decentralized feedback in the presence of interconnection and feedback delays. Based on the Lyapunov's direct approach with a four-term energy functional and a three-term quadratic formulation of the given state dynamics, this method has a larger search space than used so far. Numerical examples corroborate the superiority of this method vis-a-vis the existing ones for several subsets of the general problem.

Static Output Feedback Control for Discrete-time Piecewise Linear Systems: an LMI Approach

This paper investigates the problem of static output feedback (SOF) control for discrete-time piecewise linear systems. Based on piecewise quadratic Lyapunov functions, new sufficient LMI conditions for the synthesis of SOF stabilization controllers are presented. Meanwhile, by using Finsler's lemma, a set of slack variables with special structure are introduced to reduce design conservatism. Compared to the existing methods, the proposed method has a good performance and can work successfully in situations where the existing methods fail. An extension of this method is also given in order to incorporate H ∞ performance. Three examples are given to illustrate the effectiveness of our method.

Stabilizing adaptive controller for uncertain dynamical systems: An LMI approach

Adaptive stabilization of a class of linear systems with matched and unmatched uncertainties is considered in this paper. The proposed controller indeed stabilizes the uncertain system for any positive values of its non-adaptive gain that may be tuned to enhance dynamic response of system. The performance of uncertain system along with the Algebraic Riccati Equation that arises from the adaptive stabilizing controller is now formulated as a multi-objective Linear Matrix Inequality optimization problem. The decay rate and a factor governing the ultimate bound of the system states are considered to characterize the closed loop system performance. Finally, the effectiveness of the proposed controller is illustrated via stabilizing a mass-spring system.

Consentability and protocol design of multi-agent systems with stochastic switching topology

This paper studies the mean square consentability problem for a network of double-integrator agents with stochastic switching topology. It is proved that in Markov-switching topologies, the network is mean square consentable under linear consensus protocol if and only if the union of graphs in the switching topology set has globally reachable nodes. A necessary and sufficient condition of the mean square consensus is obtained. Finally, an LMI approach to the design of the consensus protocol is presented. Numerical simulations are given to illustrate the results.

Loose eigenstructure assignment via rank-one LMI approach with application to transient response shaping in H ∞ control

This article proposes a new regional eigenstructure assignment via rank-one LMI approach. A gain parameter condition for the regional eigenvalue/eigenstructure assignment is newly derived. This assignment condition is easily combined with H ∞ design by means of enhanced LMI characterisation. In the present approach, the desired assignment of closed-loop eigenvalues (i.e. poles) are not previously fixed but constrained into individual assignment regions to bring us more design freedom than classical exact assignment. The regional assignment discussed in this article never falls into an ordinary LMI root clustering because the union of assignment regions is disjoint in general. Each closed-loop eigenvector is also constrained into individual alignment cone. To show the practical use of the extra design freedom brought by regional assignment, a transient response shaping in H ∞ design is also discussed. A useful design algorithm based on linearisation algorithm is proposed.

Deadbeat Control for Linear Systems with State Constraints

This paper presents a deadbeat control scheme for linear systems with state constraints. The proposed controller increases the number of steps on-line for the deadbeat tracking performance, satisfying given admissible state constraints. LMI conditions are given to minimize the unavoidable step delay. The proposed schemes can be easily developed by using LMI approach, and are validated by numerical simulation.

An iterative LMI approach to H<SUB align=right>∞ networked control with random communication delays

In this paper, an iterative LMI approach is proposed to deal with the control problem for Networked Control Systems (NCSs) with random communication delays. Both random measurement and control delays are simultaneously considered due to limited communication capacity. The NCSs with both measurement and control delays are modelled as a stochastic parameter system which contains two independent Bernoulli distributed white sequence. A dynamic output controller is designed to exponentially stabilise the networked system in the sense of mean square, and also achieve the prescribed H∞ disturbance attenuation level. An iterative algorithm is developed to compute the optimal H∞ disturbance attenuation and the controller parameters. An illustrative example is provided to show the applicability of the proposed method.

Application of LMI approach to positive stabilization of 2D linear systems by state feedback

Abstract The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved by the use of LMI method. Necessary and sufficient conditions for the solvability of the problem are given. The proposed approach is illustrated by numerical example.