Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

Abstract

This paper investigates exponentially stable guaranteed cost control (GCC) for a class of nonlinear systems which is represented by Takagi-Sugeno (T-S) fuzzy systems. State feedback controllers of parallel distributed compensation (PDC) structure are designed by the means of GCC for continuous and discrete-time T-S fuzzy systems respectively. GCC methods in this paper adopt quadratic performance functions, which take effects of control efforts, regulation errors and convergence rates into consideration simultaneously, to provide desirable performance and fast response for closed-loop systems. Sufficient design conditions that guarantee exponential stabilities of resulting closed-loop systems with predefined convergence rates are presented. By setting different convergence rates, response speed of the closed-loop nonlinear system can be adjusted. The proposed design procedures are eventually

Guaranteed Cost Finite-Time Control for Positive Switched Linear Systems with Time-Varying Delays

“…Journal of Control Science and Engineering 3 Remark 9. It should be noted that the proposed cost function is different from the existing literatures [21][22][23][24]; it is for the first time introduced in positive switched systems. This definition provides a more useful description, because it takes full advantage of the characteristics of nonnegative states of positive switched systems.…”

“…There are some results about this problem; see [22][23][24][25][26][27][28][29] and references therein. These results mainly focus on nonpositive systems, involved in fuzzy systems [22,27], continuous-time nonlinear systems [23], interconnected systems [24], Markov switching systems [25], stochastic systems [26,28], neural networks [29], and so on. However, to the best of our knowledge, there are few results available on guaranteed cost finite-time control for positive switched linear systems with time-varying delays, which motivates our present study.…”

A Center Manifold Theory-Based Approach to the Stability Analysis of State Feedback Takagi-Sugeno-Kang Fuzzy Control Systems

“…Since y = x 2M , the fuzzy control system structure is illustrated in Fig. 2, where rreference input, econtrol error, i 1 and i 2fuzzy controller inputs also given in (16), and The block FC in Fig. 2 is a Takagi-Sugeno-Kang state feedback fuzzy controller, which is designed starting with a set of linear state feedback controllers to stabilize the simplified EHS model in (17) and next applying the modal equivalence principle [101] to merge the linear state feedback controllers placed in the rule consequents of FC.…”

“…The main idea in relation with the PDC-based approach to the stability analysis and stable design of Takagi-Sugeno-Kang fuzzy control systems based on LMIs is an extensive use of quadratic Lyapunov function candidates. The effect of various parameters of the fuzzy models are considered resulting in non-quadratic Lyapunov function-based approaches as, for example, the membership-function-dependent analysis [14,15], non-quadratic stabilization of uncertain systems, exponential stability with guaranteed cost control [16], piecewise continuous and smooth functions, piecewise continuous exact fuzzy models, general polynomial approaches [17,18], sum-of-squares-based polynomial membership functions [19][20][21][22], superstability conditions, integral structure based Lyapunov functions [23], the subspace-based improved sector nonlinearity approach [24], the fractional intelligent approach, and interpolation function-based approaches [25].…”

“…The additional parameters of these nonlinear systems offer increased flexibility (advantageous in case of optimal fuzzy control) but this is paid by their more complicated design and tuning if they are used as fuzzy models and controllers. Some of the important applications of type-2 fuzzy systems to fuzzy control with stability analysis and nature-inspired algorithms that ensure their optimal tuning are reported in [14,16,33] and [51][52][53][54].…”