LMI Relaxations for $$\mathcal{H }_{\infty }$$ and $$\mathcal{H }_{2}$$ Static Output Feedback of Takagi–Sugeno Continuous-Time Fuzzy Systems

Output Feedback H∞ Control Design For Polynomial T–S Systems: A Novel SOS Approach

“…Example 1: This example presents the design of a SOF H ∞ controller for a system borrowed from [23]. This example was solved using the homogeneous polynomial matrices of arbitrary and independent degrees.…”

“…This example was solved using the homogeneous polynomial matrices of arbitrary and independent degrees. Consider the two-rules T-S fuzzy system of the form (2), with the same data as in [23]:…”

“…Table I lists the values of γ min obtained from [23], [24] and Theorem 1 in this paper for different degrees. It can be easily seen that the results obtained with Theorem 1 with (2d = 2) outperform those based on C1-T2 in [23] with (g = 1, g = 2, g = 6, g = 10).…”

“…Table I lists the values of γ min obtained from [23], [24] and Theorem 1 in this paper for different degrees. It can be easily seen that the results obtained with Theorem 1 with (2d = 2) outperform those based on C1-T2 in [23] with (g = 1, g = 2, g = 6, g = 10). It can also be seen that increasing the degree of the polynomial Lyapunov function from 2d = 0 to 2d = 2 reduces significantly the norm bound γ min and hence improves the obtained performances.…”

A T–S Fuzzy Approach to the Local Stabilization of Nonlinear Discrete-Time Systems Subject to Energy-Bounded Disturbances

“…The local stability issue in T-S fuzzy models may also be related to the natural existence of constraints in the state variables of real systems, due, for example, to safe operational conditions, physical limitations or some desired level of energy consumptions, as discussed in Klug et al (2014), or related to the presence of time derivatives of the MFs in the stability analysis when dealing with continuous-time systems, as in Guerra et al (2012), Tognetti et al (2013). Further, in the presence of exogenous disturbances, the input-to-state stability properties as well as input-to-output performance criteria of nonlinear systems may hold only locally (Rapaport and Astolfi 2002).…”