Robust and Non-fragile H_∞ Control for a Class of Uncertain Jump Linear Systems

This paper describes the synthesis of robust and non-fragile H∞ state feedback controllers for a class of uncertain jump linear systems with Markovian jumping parameters and state multiplicative noises. Under the assumption of a complete access to the norm-bounds of the system uncertainties and controller gain variations, sufficient conditions on the existence of robust stochastic stability and γ-disturbance attenuation H∞ property are presented. A key feature of this scheme is that the gain matrices of controller are only based on It, the observed projection of the current regime rt.

Robust Non-fragile PID Controller Design for the Stroke Regulation of Metering Pumps

This job focuses on the stroke regulation of a class of high-precision metering pumps.A parametertuning method of robust non-fragile PID（proportional-integral-derivative）controllers is proposed with the assumption that a PID controller has additive gain perturbations.An H-infinite robust PID controller can be obtained by solving a linear matrix inequality.This approach can guarantee that the closed-loop control systems is asymptotically stable and the H-infinite norm of the transfer function from the disturbance to the output of a controlled system is less than a given constant to attenuate disturbances.The simulation case shows that the control performance of the proposed strategy is significantly better than the traditional PID approach in the situation with perturbations of controller parameters.

Non-fragile decentralized H_∞ controller design for uncertain linear systems

Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.

H_∞ Robust Fault-Tolerant Controller Design for an Autonomous Underwater Vehicle’s Navigation Control System

In order to improve the security and reliability for autonomous underwater vehicle （AUV） navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities （LMI） to solve for the Hv controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.

Robust H_∞ control for aseismic structures with uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.

Robust H_∞ control for uncertain descriptor systems with state and control delay

The problem of robust stabilization for uncertain continuous descriptor system with state and control delay is considered. The time-varying parametric uncertainty is assumed to be norm-bounded. The purpose of the robust stabilization is to design a memoryless state feedback law such that the resulting closed-loop system is robustly stable A sufficient condition that uncertain continuous descriptor system is robustly stabilizabled by state feedback law is derived in terms of linear matrix inequality （LMI）. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Robust reliable H_∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.

Improved Results on Robust H_∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is con- sidered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Robust H_∞ controller design for a class of nonlinear fuzzy time-delay systems

The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.

Delay-dependent robust H_∞control of convex polyhedral uncertain fuzzy systems

The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.

Delay-dependent robust H_∞ control for uncertain discrete time-delay fuzzy systems

The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.

LMI Approach to Robust H_∞/H_2 Controller Design with Regional Poles Constraint of a Pump-Motor System

The time domain guideposts requirements of a pump-motor system is transfered into a series of constraints which express the robust performance upper bound and regional poles limits of the closed loop system. Then the servo system control problem is transferred into the problem of robust performance optimizing under regional poles constrains described by linear matrix inequality （LMI）. These LMIs are easy to solve through the Matlab LMI-toolbox. Simulations indicate that the controller has excellent dynamic, static and disturbance rejection performance, and the control system is robust and has perfect H2 performance to the bounded external torque disturbance.

Design of decentralized robust H_∞ state feedback controller

The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H_∞ state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H_∞ performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional（LKF）, sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities（LMIs）. The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

Soft initial-rotation and H_∞ robust constant rotational speed control for rotational MEMS gyro

A novel soft initiai-rotation control system and an H∞ robust constant rotational speed controller （RCRSC） for a rotational MEMS （micro-electro-mechanical system） gyro are presented. The soft initial-rotation control system can prevent the possible tumbling down of the suspended rotor and ensure a smooth and fast initial-rotation process. After the initial-rotation process, in order to maintain the rotational speed accurately constant, the RCRSC is acquired through the mixed sensitivity design approach. Simulation results show that the actuation voltage disturbances from the internal carrier waves in the gyro is reduced by more than 15.3 dB, and the speed fluctuations due to typical external vibrations ranging from 10 Hz to 200 Hz can also be restricted to 10^-3 rad/s order.

Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.

Robust H_∞ Control of Uncertain Linear Systems with Multiple State Delays—LMI Approach

This paper deals with the problem of robust H∞ control for uncertain systems with multiple state delays. The parameter uncertainties are unknown but norm - bounded. An LMI based method is developed for robust H∞ stabilization for a class of uncertain systems with multiple state delays via linear memoryless state feedback control. The resuits depend on the size of the delays and are given in terms of linear matrix inequalities, so they are less con. servative than those of delay - independent.