This paper investigates the problem of output feedback robust $\mathscr{H}_{\infty }$ control for a class of nonlinear spatially distributed systems described by first-order hyperbolic partial differential equations (PDEs) with Markovian jumping actuator faults. The nonlinear hyperbolic PDE systems are first expressed by Takagi–Sugeno fuzzy models with parameter uncertainties, and then, the objective is to design a reliable distributed fuzzy static output feedback controller guaranteeing the stochastic exponential stability of the resulting closed-loop system with certain $\mathscr{H}_{\infty }$ disturbance attenuation performance. Based on a Markovian Lyapunov functional combined with some matrix inequality convexification techniques, two approaches are developed for reliable fuzzy static output feedback controller design of the underlying fuzzy PDE systems. It is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities based on the finite-difference method in space. Finally, two examples are presented to demonstrate the effectiveness of the proposed methods.

Fuzzy-Model-Based Reliable Static Output Feedback $\mathscr{H}_{\infty }$ Control of Nonlinear Hyperbolic PDE Systems

This paper investigates the problem of robust H∞ output-feedback control for a class of nonlinear systems under unreliable communication links. The nonlinear plant is represented by a Takagi-Sugeno (T-S) uncertain fuzzy model, and the communication links between the plant and controller are assumed to be imperfect, i.e., data-packet dropouts occur intermittently, which is often the case in a network environment. Stochastic variables that satisfy the Bernoulli random-binary distribution are adopted to characterize the data-missing phenomenon, and the attention is focused on the design of a piecewise static-output-feedback (SOF) controller such that the closed-loop system is stochastically stable with a guaranteed H∞ performance. Based on a piecewise Lyapunov function combined with some novel convexifying techniques, the solutions to the problem are formulated in the form of linear matrix inequalities (LMIs). Finally, simulation examples are also provided to illustrate the effectiveness of the proposed approaches.

Fuzzy-Model-Based Piecewise ${\mathscr H}_{\infty }$ Static-Output-Feedback Controller Design for Networked Nonlinear Systems

This paper investigates the problem of robust H∞ output feedback control for a class of continuous-time Takagi-Sugeno (T-S) fuzzy affine dynamic systems with parametric uncertainties and input constraints. The objective is to design a suitable constrained piecewise affine static output feedback controller, guaranteeing the asymptotic stability of the resulting closed-loop fuzzy control system with a prescribed H∞ disturbance attenuation level. Based on a smooth piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexification techniques, some new results are developed for static output feedback controller synthesis of the underlying continuous-time T-S fuzzy affine systems. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, three examples are provided to illustrate the effectiveness of the proposed methods.

Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions

More than 40 years after fuzzy logic control appeared as an effective tool to deal with complex processes, the research on fuzzy control systems has constantly evolved. Mamdani fuzzy control was originally introduced as a modelfree control approach based on expert?s experience and knowledge. Due to the lack of a systematic framework to study Mamdani fuzzy systems, we have witnessed growing interest in fuzzy model-based approaches with Takagi-Sugeno fuzzy systems and singleton-type fuzzy systems (also called piecewise multiaffine systems) over the past decades. This paper reviews the key features of the three above types of fuzzy systems. Through these features, we point out the historical rationale for each type of fuzzy systems and its current research mainstreams. However, the focus is put on fuzzy model-based approaches developed via Lyapunov stability theorem and linear matrix inequality (LMI) formulations. Finally, our personal viewpoint on the perspectives and challenges of the future fuzzy control research is discussed.

Fuzzy Control Systems: Past, Present and Future

This paper addresses the issue of robust fuzzy sliding mode control for continuous-time nonlinear Takagi–Sugeno fuzzy systems with semi-Markovian switching. The focus is on designing a novel fuzzy integral sliding surface without assuming that the input matrices are the same with full column rank and then developing a fuzzy sliding-mode controller for stochastic stability purpose. Based on Lyapunov theory, a set of newly developed linear matrix inequality conditions are established for stochastic stability of the sliding-mode dynamics with generally uncertain transition rates, and then extended to where the input matrix is plant-rule-independent, as discussed in most existing literatures. Furthermore, finite-time reachability of the sliding surface is also guaranteed by the proposed fuzzy sliding-mode control laws. A practical example is provided to demonstrate the effectiveness of the established method numerically.

A Novel Robust Fuzzy Integral Sliding Mode Control for Nonlinear Semi-Markovian Jump T–S Fuzzy Systems

Robust H∞ fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties

This paper investigates the problem of H/spl infin/ control for T-S fuzzy discrete-time descriptor systems. Firstly, an analysis result for H/spl infin/ control is derived and characterized by a set of linear matrix inequalities (LMIs). The derived analysis condition is then applied to design an H/spl infin/ 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 H control. The difficulty is overcome by the approach proposed in this paper. Before this presentation, no result about the H/spl infin/ 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.

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

This paper proposes a new approach to solve robust H ∞ control problems for uncertain continuous-time descriptor systems. Necessary and sufficient conditions for robust H ∞ control analysis and design are derived and expressed in terms of a set of LMIs. In the proposed approach, the uncertainties are allowed to appear in all system matrices. Furthermore, a couple of assumptions that are required in earlier design methods are not needed anymore in the present one. The derived conditions also include several interesting results existing in the literature as special cases.

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An Improvement on Robust H∞ Control for Uncertain Continuous-Time Descriptor Systems

This paper proposes a new LMI approach to establish a more relaxed sufficient condition for quadratic stabilization of T-S fuzzy systems. The proposed conditions not only improve the conservativeness but also include previous results as special cases. Extending the proposed idea to deal with the observer-based H ∞ control problem, two conditions that guarantee the existence of the H ∞ controller based on fuzzy observers are also developed. The conditions are more relaxed than the existing one and ensure the designed fuzzy H ∞ controller achieving a better performance. The validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous-time nonlinear system.

Stabilization and observer-based H ∞ control for T-S fuzzy systems — An improved LMI approach

This paper considers robust H/spl infin/. control problem for interval descriptor systems. Necessary and sufficient LMI-based conditions are derived for robust H/spl infin/ control analysis of interval descriptor systems. Using the analysis result, feedback controllers are designed so that the closed-loop interval descriptor systems are admissible and their transfer matrices have H/spl infin/-norm bounded by a prescribed value. This paper seems the first one attempting to deal with robust H/spl inifn/ control problem of interval descriptor systems.

Hung-Jen Lee

Papers

Robust H∞ fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties

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

An Improvement on Robust H∞ Control for Uncertain Continuous-Time Descriptor Systems

Stabilization and observer-based H ∞ control for T-S fuzzy systems — An improved LMI approach

Robust H/spl infin/ Control for Interval Descriptor Systems