Decentralized H∞ suboptimal design: An LMI approach

Address the design of state-feedback H_∞ suboptimal controllers. Through parameterization of decentralized controllers, the design condition for the feedback gain is given in the form of a biaffine matrix inequality. An iterative algorithm based on linear matrix inequality(LMI) is proposed to obtain the decentralized controller which ensures the closed-loop system asymptotically stable and the H_∞-norm less than constant number 1. Project supported by the National Natural Science Foundation of China Synopsis of the first author Gui Weihua, professor, born in 1950. Majoring in complex metallurgical process modeling and optimal control theory and application of large-scale system, modern robust control, computer control system.     

Decentralized H∞ state feedback control for large-scaleinterconnected uncertain systems with multiple delays

Decentralized H∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition which makes the closed-loop system decentralized asymptotically stable with H∞ performance was derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities. The method overcomes the limitations of the existing algebraic Riccati equation method. Finally, a numerical example was given to demonstrate the design procedure for the decentralized H∞ state feedback controller.     

State space methods for decentralized H∞ control

This paper presents state space methods for decentralized H_∞ control, which contain two respects: a parametrization approach and an iterative algorithm. For large scale systems withN subsystems, decentralized H_∞ controllers can be derived by a parametrization result for centralized H_∞ controllers and designed by an iterative algorithm with structured constraint to the controllers. Project supported by the National Natural Science Foundation of China Synopsis of the first author Wu Min, professor, born in July, 1963, research interests are in robust control, digital control systems theory, nolinear control systems and industrial process contnol.     

The iterative linear matrix inequality suboptimal design of decentralized ∞ control

An approach is proposed to design decentralized state feedback _∞ suboptimal controllers for LTI interconnected large scale systems. The parametrization theorem of decentralized robust state feedback controllers is developed in two steps and the design condition for the feedback gain is in the form of matrix inequalities. An iterative solution algorithm based on linear matrix inequality (LMI) techniques is proposed to obtain the decentralized feedback gain. The given examples are taken to show the application and the convergence of the algorithm. Project supported by the National Natural Science Foundation of China Synopsis of the first author Xie Yongfang, Doctoral student, born in 1972, majoring in _∞ control theory and its application, modem robust control, decentralized control.     

Non-fragile delay-dependent H ∞ control of linear time-delay system with uncertainties in state and control input

The problem of designing a non-fragile delay-dependent H∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral inequality method and Lyapunov-Krasovskii stability theory were used to derive new delay-dependent bounded real lemmas for a non-fragile state-feedback controller containing additive or multiplicative uncertainties. They ensure that the closed-loop system is internally stable and has a given H∞ disturbance attenuation level. Then, methods of designing a non-fragile H∞ state feedback controller were presented. No parameters need to be tuned and can be easily determined by solving linear matrix inequalities. Finally, the validity of the proposed methods was demonstrated by a numerical example with the asymptotically stable curves of system state and controller output under the initial condition of x（0）=[1 0 -1]^T and h=0.8 time-delay boundary.     

Dynamic extending nonlinear H∞ control and its application to hydraulic turbine governor

There exists a large class of nonlinear systems with uncertainties, such as hydraulic turbine governors, whose robust control problem is hard to solve by means of the existing robust control approaches. For this class of systems, this work presents a dynamic extending H∞ controller via both differential geometry and H∞ theory. Furthermore, based on differential game theory, it has been verified that the proposed control strategy has robustness in the sense that the disturbance can be attenuated effectively because the L2-gain from the disturbance input to the regulation output signal could be reduced to any given level. Thirdly, a robust control strategy for hydraulic turbine governor is designed according to the proposed extending H∞ control method, and has been developed into a real control equipment. Finally the field experiments are carried out which show clearly that the developed control equipment can enhance transient stability of power systems more effectively than the conventional controller.     

Linearization of T-S fuzzy systems and robust H_∞ control

Takagi-Sugeno (T-S) fuzzy model is difficult to be linearized because of membership functions included. So, novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system. The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models. The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily. After the linearization of T-S fuzzy model, a robust H _∞ controller with the robustness of sliding model control (SMC) is designed. As a result, controlled T-S fuzzy system shows the performance of H _∞ control and the robustness of SMC.     

Delay-independent decentralized H ∞ control for multi-channel discrete-time systems with uncertainties

A robust decentralized H∞ control problem was considered for uncertain multi-channel discrete-time systems with time-delay. The uncertainties were assumed to be time-invariant, norm-bounded, and exist in the system, the time-delay and the output matrices. Dynamic output feedback was focused on. A sufficient condition for the multi-channel uncertain discrete time-delay system to be robustly stabilizable with a specified disturbance attenuation level was derived based on the theorem of Lyapunov stability theory. By setting the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller, the problem was reduced to a linear matrix inequality （LMI） which is sufficient to existence condition but much more tractable. An example was given to show the efficiency of this method.     

An LMI-based unified approach to reduced-order controller design

The design of reduced-order controllers is considered for stabilization control, covariance upper bound control, linear quadratic regulator, ∞ control, H∞ control, positive real control problems and robust H2 control, robust ∞ control and robust H∞ control problems for generalized linear plants without any additional assumptions. An upper bound of the order is obtained with which the (robust) controllers can guarantee stability constraints and satisfy the same design objectives as the so-called "full-order" controllers. A unified linear-matrix-inequality ( LMI) based approach to reduced-order (robust) controller design for all the above-mentioned problems is provided. It us shown that each of these problems is solvable if and only if two uncoupled LMIs with an LMI-type constraint have a pair of positive definite solutions, one of which has a lower dimension than that given by Skelton and iwasaki (1995). All desired reduced-order (robust) controllers are parameterized via the solutions of LMIs Moreov     

H∞ control of an active suspension system

An H_∞ controller for an active suspension system is designed, which has taken the performance of ride comfort and the system robustness into account. Simulation results show that a concentrated weighting of the car body acceleration output, for the frequency where human being are most sensitive to vibration, has been executed by introducing the frequency dependent weighing function, thus the suspension acceleration frequency response characteristic can be improved. It is also pointed out that the designed controller is effective in the system robustness against the fluctuation of parameter of system. Project supported by the Natural Science Foundation of Hunan Province Synopsis of the first author Liu Shaojun, professor, born on Nov. 14, 1955, majoring in automation and mechanical engineering.