More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

Abstract

This paper proposes more relaxed stabilization conditions based on a non‐quadratic Lyapunov function (NQLF) and parallel distributed compensator (PDC) controller. The conditions are derived in terms of linear matrix inequalities (LMIs) by introducing three slack matrices based on the properties of TS membership functions, an open loop system and a PDC controller. These slack matrices are utilized to decouple the LMI variables from the TS system and the input matrices. Therefore, the proposed approach greatly reduces the number of LMI conditions and improves feasibility by providing more degrees of freedom compared to recently published studies. Moreover, local stability and stabilization conditions are considered to handle the time derivatives of membership functions appearing in the stabilization synthesis of the TS closed‐loop system with PDC controller. Finally, several examples are presented to demonstrate the advantages of the proposed approaches.

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

“…, where a and b are two scalar parameters and take different values. For each value of the parameters, the proposed approach, QLF-based approach, 5 LMI-based NQLF, 45 ILMI-based NQLF, 17 and sequential LMI 23 are deployed to check whether these approaches provide feasible solutions or not. Figure 1 illustrates the feasibility region of different control design methods.…”

Adaptive TS Fuzzy-Based MPC for DC Microgrids With Dynamic CPLs: Nonlinear Power Observer Approach

“…This section deals with the design of a nonlinear MPC scheme based on the TS fuzzy model. The aggregation of the MPC technique with fuzzy methods [26]- [29] brings about a simple but effective control strategy. In this section, the designing of a nonlinear MPC controller based on the TS fuzzy model of the system is provided.…”

Synchronization Analysis of Complex Dynamical Networks Subject to Delayed Impulsive Disturbances

“…Complex networks are composed of a large number of highly interconnected dynamical units and are used to describe various practical systems, such as social interacting species, transportation networks, biological and chemical systems, and neural networks [1][2][3][4][5][6][7][8]. As a type of complex networks, coupled neural networks have received great attention and a lot of previous studies mainly focused on stability and stabilization analysis [9][10][11][12][13].…”