This paper proposes robust H∞ output feedback control stabilization for uncertain Takagi– Sugeno (T-S) fuzzy systems via linear matrix inequalities (LMIs). In order to reduce the conservatism associated with T-S fuzzy system, a new form of non-monotonic Lyapunov functions is used. In the non-monotonic approach, the monotonic decrease of the Lyapunov function is relaxed which enables it to increase locally but vanish eventually. Based on the non-monotonic Lyapunov function approach, sufficient conditions for the existence of robust H∞ output feedback control stabilization are derived. The proposed design technique is shown to be less conservative than the existing non-monotonic approach, namely, 𝑘-samples variations of Lyapunov function. The effectiveness of the proposed approach is further illustrated via numerical example.

This paper presents a new control method based on Lyapunov function approach for simultaneous control of grid currents, circulating currents and modules voltages of a modular multilevel converter. Unlike existing methods that use nested and multi-loop control structures, the proposed method has a single-loop structure and ensures the global asymptotic stability of the closed-loop system. In this regard, first, the dynamic equations of the converter and the grid are extracted using the averaging technique, and then the coordinates of the steady-state operating point are calculated. Next, using the obtained operating point coordinates and the dynamic equations of the main system, the error dynamics are computed. Finally, these equations and the Lyapunov function, based on the error signals, are used for the analytic calculation of the control inputs. The simulation results confirm the efficiency of the proposed control method.

In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via rational Lyapunov function is investigated. One of the methods for estimating DA is to find the greatest level set. In this study, in order to obtain the greatest level set, cost function based on increasing the region enclosed to the level set has been offered instead of using shape factor.Estimating DA has been converted into solving bilinear matrix inequality optimization problem.Capacity of this method compared to other methods in recent studies has been shown through some examples.

This paper proposes a sliding mode observer (SMO) for actuator fault reconstruction of nonlinear systems subjected to external disturbance. In the proposed approach, first, the nonlinear system is modelled by a Takagi-Sugeno fuzzy model with immeasurable premise variables. Then, SMO is used to estimate the states and fault. Finally, by using a non-quadratic Lyapunov function (NQLF), the stability of the error system is proved. By considering performance criteria, the effect of the exogenous disturbance on the state estimations is minimized which provides effective fault estimation. Furthermore, the states and fault estimations asymptotically converge to their actual values for the non-perturbed systems. In the stability analysis and the observer gains design, some change of coordinates are proposed which the transformation matrix of one of them is obtained by solving linear matrix inequalities (LMIs). The proposed approach has some superiority over the existing methods. First, employing the NQLF leads to more relaxed results and better estimation performance. Second, using SMO for fault reconstruction makes the proposed approach insensitive to the uncertainties and unknown inputs and besides detecting the fault, its shape and size are determined. Third, since the premise variables are assumed to be unmeasurable, the presented approach is applicable for a wide class of nonlinear systems. Finally, a continuous stirred tank reactor (CSTR) process is considered and numerical simulation is carried out to illustrate the effectiveness and the accuracy of the proposed approach comparison with the recently published methods.

This paper presents a new approach to estimate and to enlarge the domain of attraction for a planar continuous-time piecewise affine system. Various continuous Lyapunov functions have been proposed to estimate and to enlarge the system’s domain of attraction. In the proposed method with a new vision and with the aids of a discontinuous piecewise quadratic Lyapunov function, the domain of attraction at the origin is enlarged by designing a state feedback controller. This paper shows that the continuity of the Lyapunov function on the boundaries, increases the conservativeness in estimating the domain of attraction, and gives more powerful search ability to the domain of attraction estimation algorithm by relaxing this continuity condition. The simulation results show the superiority of the proposed method so that using this method the larger estimation of the domain of attraction is obtained than continuous one.

In this study, a hierarchical fuzzy controller associated with PD classical controller with feedback error learning method for class of canonical SISO nonlinear system in presence of bounded disturbance is presented. The stability of whole system is guaranteed through a Lyapunov function. The adaptation laws of all parameters of consequent part of hierarchical fuzzy system are derived using it. Tunable parameters of hierarchical fuzzy system are appeared in nonlinear form at the output. Using the mentioned theorem, they are appeared in linear form. There is an upper bound for the residual terms. They are considered in Lyapunov function and the adaptation law is derived for them. It is shown that, the proposed theorem is applicable to the hierarchical fuzzy system with any structure and any number of layers and even to the ordinary fuzzy systems. Also, using hierarchical fuzzy controllers leads to reduction of number of rules and parameters in a fuzzy system. Finally, the proposed method is applied on two systems (flexible joint robot and quarter active suspension system). The results are compared with classical sliding mode method. They reveal the efficiency of the suggested algorithm.