Relaxed Stabilization and Disturbance Attenuation Control Synthesis Conditions for Polynomial Fuzzy Systems

Policy iteration forH∞control of polynomial time‐varying systems

“…In [25], it has been shown that one can efficiently relax the Bellman equation to an SOS optimization problem. Many of other problems in control theory, such as optimal control of discrete‐time systems [26], H ∞ control of polynomial [27], polynomial fuzzy [28], and uncertain polynomial systems [29], mixed H 2 / H ∞ control design [30], H ∞ control of polynomial systems with adjustable parameters ( H ∞ codesign) [31], multi‐objective control design [32], and constrained states control [33], have been solved with the idea of SOS‐based ADP.…”

Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T–S Fuzzy Systems

“…In some solutions, the MFDs are divided into piecewise linear functions in [25] and [26], which introduces derivative information into the stability analysis and less conservative results are obtained. Moreover, some scholars use polynomial MFs method to incorporate more detailed MFs information into sum-of-squares (SOS)-based stability conditions, as in [27], [28]. To further analyze the conservativeness of stability conditions with MF information, a MF transformation approach was proposed in [29], where the main idea was to involve MFs in a convex combination surrounded by several sample points in membership space.…”

Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints

“…Despite its effectiveness for nonlinear control, TS fuzzy-model-based approaches still suffer major drawbacks on design conservatism and numerical complexity in dealing complex nonlinear systems. To reduce the conservatism caused by the use of common quadratic Lyapunov functions, many other alternative classes of Lyapunov function candidates have been proposed such as piecewise Lyapunov functions [6], [7], line-integral fuzzy Lyapunov functions [8], [9], and fuzzy Lyapunov functions [10]- [12], see [2] for a recent review. Moreover, it has been demonstrated that fuzzy Lyapunov functions are especially effective for conservatism reduction in discrete-time TS fuzzy control framework [13], [14].…”

“…Although the local linearity of N-TS fuzzy systems is not preserved, exploiting judiciously the absolute stability theory [3] enables a tractable control framework when the local retained nonlinearities verify some sector-bound properties [15], [17]- [22]. Note that TS fuzzy systems with polynomial consequents have been also discussed [9], [23], [24]. Using Lyapunov stability theorem, sufficient design conditions were derived in the form of sum-of-squares constraints, see [9], [24] and references therein.…”

“…Note that TS fuzzy systems with polynomial consequents have been also discussed [9], [23], [24]. Using Lyapunov stability theorem, sufficient design conditions were derived in the form of sum-of-squares constraints, see [9], [24] and references therein.…”