Jun Yoneyama

Output stabilization of Takagi-Sugeno fuzzy systems

Abstract In this paper the output stabilization problem of Takagi–Sugeno fuzzy models is considered. First a natural form of observers for such models is given. Sufficient conditions for their asymptotic convergence are given which are dual to those for the stability of state feedback fuzzy controllers. We then show that a state feedback controller and an observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the Lyapunov method using positive definite matrices. In this sense it is shown that the separation principle holds for Takagi–Sugeno fuzzy systems. Two design examples are given to illustrate the theory.

Design of output feedback controllers for Takagi—Sugeno fuzzy systems

Abstract In this paper the design problem of output feedback controllers for Takagi–Sugeno fuzzy models is considered. As for the premise variables, we consider two cases: the outputs and the state variables. In each case, we first consider the design of observers. In the first case we give sufficient conditions for the asymptotic convergence of the fuzzy observers. In the second case we give observers for an approximation of the original system. We then propose the output feedback controllers based on state feedback controllers and observers. Two design examples are given to illustrate the theory.

Robust stability and stabilization for uncertain Takagi--Sugeno fuzzy time-delay systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability and robust stability for a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems. We first consider robust stability conditions of uncertain fuzzy systems. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time delay, and are given in linear matrix inequalities(LMIs). An appropriate selection of Lyapunov-Krasovskii function and introduction of free weighting matrices generalize robust stability conditions. Next, we consider the stabilization problem with memoryless and delayed feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give two examples that illustrate our results. We compare our conditions with other stability conditions and show our conditions are rather generalized.

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

New delay-dependent approach to robust stability and stabilization for Takagi--Sugeno fuzzy time-delay systems

In this paper, we consider new generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy time-delay systems. In the literature, both delay-independent stability conditions and delay-dependent stability conditions for fuzzy time-delay systems have already been obtained. However, those conditions are rather conservative and do not guarantee a wide stability region. This is also true in case of the robust stability for uncertain fuzzy time-delay systems. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain generalized delay-dependent stability conditions. In fact, these techniques lead to generalized and less conservative stability conditions that guarantee a wide stability region. Our delay-dependent stability conditions thus obtained are given in terms of linear matrix inequalities (LMIs). We give three examples to illustrate our results. Comparison with other stability conditions in the literature shows our conditions are the most powerful ones to guarantee the widest stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques obtained for the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems. Moreover, we give a design method of robustly stabilizing controllers for uncertain Takagi-Sugeno fuzzy time-delay systems.

H/sub /spl infin//-control for Takagi-Sugeno fuzzy descriptor systems

The design problem of output feedback H/sub /spl infin// controllers for Takagi-Sugeno fuzzy descriptor models is considered. We first give the sufficient conditions for the admissibility of the Takagi-Sugeno fuzzy descriptor systems. Then we introduce the H/sub /spl infin//-performance (norm) for a stable fuzzy descriptor system and give a sufficient condition for the norm being less than a given number. We also consider the H/sub /spl infin//-problem with output feedback controllers. As for the premise variable in the if-then rules, we consider three cases where the premise variable is a given function, the output, and the descriptor variable of the underlying system.

Robust H∞ control analysis and synthesis for Takagi-Sugeno general uncertain fuzzy systems

Abstract In this paper robust H ∞ control for Takagi–Sugeno general uncertain fuzzy systems where uncertainties come into all the system matrices is considered. The main result is to establish equivalent relationships between quadratic stability and quadratic stability with H ∞ disturbance attenuation γ of general uncertain fuzzy systems and H ∞ control for fuzzy systems without uncertainty. These relationships imply that quadratically stabilizing controllers and quadratically stabilizing controllers with H ∞ disturbance attenuation γ for general uncertain fuzzy systems can be obtained by designing H ∞ controllers for fuzzy systems without uncertainties. We first give sufficient conditions for the H ∞ norm being less than a given number. We then consider a general H ∞ problem with output feedback controllers, and give a design method of H ∞ controllers and sufficient conditions which guarantee the required H ∞ performance of the closed-loop system. This design method can be applied to quadratic stabilizing controllers and quadratic stabilizing controllers with H ∞ disturbance attenuation γ for general uncertain fuzzy systems. Next we analyze quadratic stability and quadratic stability with H ∞ disturbance attenuation γ of general uncertain fuzzy systems and establish equivalent relationships to H ∞ control of fuzzy systems without uncertainties. Based on these relationships, we design robust controllers for uncertain fuzzy systems. Finally, examples are given to illustrate the theory.

Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach

This paper is concerned with robust sampled-data stabilization for uncertain fuzzy systems. The system is modeled as a continuous-time fuzzy system, while the control input is a zero-order sampled-data signal. When a zero-order control input is considered, the closed-loop system can be seen as an input delay system. Hence, an input delay system approach is introduced for sampled-data control design. Sufficient stability conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Under the assumption that sampling interval is not greater than some prescribed number, stability conditions for fuzzy time-delay systems are given by using Jensens Inequality, which simplifies conditions with less matrix variables. A design method of robust sampled-data state feedback controller for uncertain fuzzy systems is then proposed. Numerical examples are given to illustrate our robust sampled-data state feedback control design and to show the effectiveness over other existing results.

Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays

In this paper, we consider delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed delays. Although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained, almost no stability condition for fuzzy systems with distributed delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed delays. Here we employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of fuzzy systems with discrete and distributed delays. We introduce some free weighting matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative stability conditions. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we give two examples to illustrate our results. Delay-dependent stability conditions obtained here are shown to guarantee a wide stability region.

Design of H∞-control for fuzzy time-delay systems

Abstract In this paper the design problems of H ∞ output feedback controllers for Takagi–Sugeno fuzzy time-delay systems are considered. We first introduce Takagi–Sugeno fuzzy time-delay systems and the H ∞ -performance (norm) for stable fuzzy time-delay systems. We consider systems with multiple time-delays in state. We give a sufficient condition for the norm being less than a given number. We then consider the H ∞ -problems with output feedback controllers. Both memoryless controller and controller with memory are considered. In the design of output feedback controllers, the selection of the premise variables in the If–Then rules is important. As for the premise variable we consider three cases where the premise variable is a given function, the output and the state of the underlying system. In the first two cases we give a design method of H ∞ -controllers and sufficient conditions which guarantee the required H ∞ -performance of the closed-loop system. In the last case we give an H ∞ -controller for an approximation of the original system. Two examples are given to illustrate the theory.