Chun-Hsiung Fang

A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems

This paper proposes a new quadratic stabilization condition for Takagi-Sugeno (T-S) fuzzy control systems. The condition is represented in the form of linear matrix inequalities (LMIs) and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature. A rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases. In comparison with conventional conditions, the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design. The latter design work is quite hard for T-S fuzzy control systems. Based on the LMI-based conditions derived, one can easily synthesize controllers for stabilizing T-S fuzzy control systems. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous-time nonlinear system.

A new LMI condition for robust stability of discrete-time uncertain systems

In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to show that an interesting result appeared recently is a special case of the proposed condition. Numerical examples also demonstrate the merit of the present condition in the aspect of conservativeness over other results in the literature.

Robust stability of generalized state-space systems

The robustness issue of uncertain generalized state-space systems is investigated. The uncertainties, in polynomial matrix form, appear on not only the state matrix but the derivative state matrix. Based on the linear fraction transformation (LFT) technique, exact bounds of the allowable perturbations for simultaneously preserving regularity, impulse elimination, and stability can be easily obtained by checking stability of some real points only. For the stability robustness issue of generalized state-space systems subject to the considered class of uncertainties, the paper presents the most general result in the literature.

H/spl infin/ Control for Discrete-Time Fuzzy Descriptor Systems

This paper investigates the problem of Hinfin control for T-S fuzzy discrete-time descriptor systems. Firstly, an analysis result for Hinfin control is derived and characterized by a set of linear matrix inequalities (LMIs). The derived analysis condition is then applied to design an Hinfin fuzzy controller. In T-S fuzzy discrete-time descriptor systems, due to singularity of E-matrix, Schur complement cannot be applied to solve the nonlinear Lyapunov inequality anymore for Hinfin control. The difficulty is overcome by the approach proposed in this paper. Before this presentation, no result about the Hinfin control of T-S fuzzy discrete-time descriptor systems is available in the literature, the paper seems the first one to tackle it from the theoretical aspect.

Robust D-stability of generalized state-space systems with one-parameter uncertainties

The robust D-stability problem for generalized state-space systems with uncertainties in the form of one-parameter family of matrices is investigated in the paper. The maximal bounds of perturbations for simultaneously preserving the regularity, impulse-immunity, and D-stability are analytically derived.

Robustness of pole-retention inside specified regions for interval descriptor systems

A sufficient condition is given to ensure that all finite poles of interval descriptor systems are retained inside specified regions. The proposed criterion also guarantees the robustness of impulse elimination. The merit of the proposed approach is clearly displayed in the calculation of robustness bounds for an uncertain liquid-level control system.

Robust H2 control analysis and design for continuous-time interval state-space systems

Abstract This paper considers the robust H 2 control problem of continuous‐time interval state‐space systems. A necessary and sufficient LMI‐based condition is derived for analysis of quadratic stability and robust H 2 control. Using the analysis result, a state feedback controller and a static output feedback controller can be designed so that the closed‐loop interval state‐space system is quadratically stable and all its transfer matrices have an H 2‐norm bounded by a prescribed value. Two LMI‐based conditions are derived respectively for the solvability of the above design problems. To the best of the authors’ knowledge, the results of robust H 2 performance of interval state‐space systems is scarce in the literature. This paper seems the first one attempting to deal with robust H 2 control analysis and design of interval state‐space systems.

Output Feedback Controllers Synthesis with Practical Pole Clustering for Descriptor Systems

The sufficient and necessary conditions for the poles of the closed-loop descriptor systems to locate in an LMI region are given in this paper in terms of only one positive definite matrices P. Hence the controller gain matrix K can be obtained explicitly. Compared to the literature, the exact eigenstructure assignment problem for descriptor systems is usually solved via extremely constrained procedures. On the other hand, for the LMI region pole clustering problem, the solvable conditions are expressed in terms of two positive definite matrices P and Q. Consequently, the controller gain matrix K can not be obtained explicitly. An example has been solved in the literature using a complicated procedure of eigenstructure assignment is solved significantly easier as a demonstration

Eigenvalue assignment inside a disk for generalized state-space systems

The problem of eigenvalue assignment inside a disk for generalized state-space systems is investigated. A necessary and sufficient condition, formulated in the linear matrix inequality form, for eigenvalue clustering inside a specified disk is derived. Then, based on the condition, a state feedback gain is synthesized to ensure not only the closed-loop system is regular and impulse-free but all its finite eigenvalues lie in a specified open disk. For standard state-space systems, the above same problems are dealt with by solving the Lyapunov equation and the Riccati equation whose solutions are positive definite. However, we indicate that for generalized state-space systems the corresponding solutions are not positive definite any more.