This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.

https://ir.nctu.edu.tw:443/bitstream/11536/13302/1/000232084300018.pdf

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems

This paper extends the Takagi-Sugeno (T-S) fuzzy model representation to analyze the stability of interconnected systems in which there exist time delays in subsystems. A novel stability criterion which can be solved numerically is presented in terms of Lyapunov's theory for fuzzy interconnected models. In this paper, we use linear difference inclusion (LDI) state-space representation to represent the fuzzy model. Then, the linear matrix inequality (LMI) optimization algorithm is employed to find common solution and then guarantee the asymptotic stability.

Fuzzy logic derivation of neural network models with time delays in subsystems

http://ynucc.yu.ac.kr/~jessie/temp/amc04_1.pdf

Robust non-fragile control for uncertain discrete-delay large-scale systems with a class of controller gain variations

In this paper, a hybrid method which combines the Adomian decomposition method (ADM), the Laplace transform algorithm and the Pade approximant is introduced to solve the approximate analytic solutions of the nonlinear Riccati differential equations. This hybrid method demonstrates accurate and reliable results, and has a great improvement in the ADM truncated series solution which diverges rapidly as the applicable domain increases. Three examples herein are given to demonstrate good accuracy and fast convergence in comparison with the exact solution.

An approximate analytic solution of the nonlinear Riccati differential equation

The present paper is concerned with the decentralized stabilization problem for a class of large-scale systems with time-varying interconnected matrices and nonlinear uncertainties. A new sufficient condition is proposed for asymptotically stabilizing the large-scale perturbed systems with a prescribed stability degree by using decentralized state-feedback controllers. All the information needed here is only the possible bounds of the time-varying interconnected matrices and nonlinear uncertainties. This condition is shown to be less conservative than the ones reported recently. The results can be extended to a class of large-scale systems with delays. Two illustrative examples are included to demonstrate the superiority of the obtained results.

Robust stabilization of large-scale systems with nonlinear uncertainties via decentralized state feedback

In this paper, the robust stability testing problem is addressed for continuous large‐scale uncertain systems with time delays in interconnections. Three classes of system uncertainties are examined: (i) nonlinear time‐varying uncertainties; (ii) linear unstructured uncertainties; and (iii) linear highly structured uncertainties. By applying the Lyapunov stability theorem, several new delay‐independent sufficient conditions are established in terms of concise inequalities, which can maintain the stability of continuous large‐scale uncertain time‐delay systems. Finally, illustrative examples are given to demonstrate the application of the results presented here.

On the robust stability for continuous large-scale uncertain systems with time delays in interconnections

Based on the Lyapunov stability theorem associated with induced norm of matrix and matrix measure techniques, this paper addresses the robust stability analysis for linear time-delay systems with uncertainties. Several new criteria, expressed by concise inequalities, are presented to guarantee the robust stability and stability with a specified decaying rate for the above systems. Both nonlinear norm-bounded and highly structured parametric uncertainties are discussed. Finally, the superiority of the proposed results is demonstrated in the illustrative examples by comparing with those available in the literature

On the robustness of stability for uncertain time-delay systems

This paper intends to derive a sufficient condition for the robust stability analysis of interval systems with multiple time-varying delays. An evolutionary programming (EP) approach is presented for solving an eigenvalue location optimization problem, which will be defined later, such that the robust stability of interval time-delay systems can be ensured. Some systems considered in the previous reports are included as special cases. Examples are given to verify our method which yields less conservative results than those appeared in the literature.

Robust stability analysis of interval systems with multiple time-varying delays: Evolutionary programming approach

Based on Lyapunov stability theory associated with transformation techniques, the D-stability robustness problem is first discussed for discrete large-scale systems subjected to interconnections and perturbations. Three classes of perturbation are treated: (1) unstructured parametric perturbations; (2) highly structured parametric perturbations; and (3) nonlinear perturbations. If all the eigenvalues of each nominal subsystem are located inside the specified discs D i (α i , r i ), respectively, sufficient conditions for D-stability are presented to guarantee that all the eigenvalues of each perturbed subsystem remain inside the same discs

Fan Chu Kung

Papers

Robust stabilization of large-scale systems with nonlinear uncertainties via decentralized state feedback

On the robust stability for continuous large-scale uncertain systems with time delays in interconnections

On the robustness of stability for uncertain time-delay systems

Robust stability analysis of interval systems with multiple time-varying delays: Evolutionary programming approach

Robustness of d-stability for discrete large-scale uncertain systems