Robust Static Output Feedback H2/H∞ Control Synthesis with Pole Placement Constraints: An LMI Approach

Robust Static Output Feedback Stabilization of Linear Systems Using Dissipativity Theory

“…Consider the open-loop unstable system recently analyzed as the first numerical example of Behrouz et al (2021), where the two vertices are given by the following matrices ,…”

“…The designed SOF stabilized the system, then the effectiveness of the strategy on the stabilization is verified. Behrouz et al (2021) also proposed a strategy for SOF stabilization of uncertain LTI systems. While we consider a lower bound on the decay rate, they consider the constraint on the closed-loop pole location.…”

“…Also, as in our work, they do not impose any restriction on the output matrix. However, Theorem 1 from Behrouz et al (2021) employs more decision variables (d.v.) for the design of the SOF than the strategy presented herein, as shown in Table 1, thus being more numerically complex to solve.…”

Dissipativity-based $\mathcal{L}_2$ gain-scheduled static output feedback design for rational LPV systems

“…Recently, a GS-SOF design for LPV systems was developed in a two stage method, where it is necessary designing a non-scheduled static feedback in the first stage [12]. In [13], a GS-SOF non-iterative design procedure with H 2 /H ∞ performance has been developed. However, as it is common in the field, these strategies consider the polytopic approach, then the LPV system can only be affine on the parameter.…”

“…Consider an LPV system as follows, − ρ x + (1 + ρ)u, y = 1 + ρ ρ x. (38) with ρ ∈ [0 1].Replacing the limits of ρ in the system, we obtain the same two vertices system of Example 2 from[13]. Consider a DAR of system (38) withπ = ρx 1 ρx 2 ρu ρw , B 3 = 1, B 4 = C 3 = 0, = 0 −1 1 0 , C 1 = A 3 , C 2 = 1 1 0 0 , Υ 2 = −I 4 , Υ 3 = 0 0 ρ 0 , Υ 4 = 0 0 0 ρ .By applying the optimization problem (36) with β = −29.3, we obtain the gain-scheduled SOF(30), with matrices K 1 = −29.0522, K 2 = −29.2994, that guarantees closed-loop stability with L 2 -gain bounded by γ = 5.2637.…”