Corrigendum to: Computing multiple Lyapunov-like functions for inner estimates of domains of attraction of switched hybrid systems: Computing multiple Lyapunov-like functions for inner estimates of domains of attraction of switched hybrid systems (International Journal of Robust and Nonlinear Control, (2018), 28, 17, (5191-5212), 10.1002/rnc.4280)

For constraint (12) in Section 4.1 and constraint (28) in Section 5.2 in the original paper, s_{9,i, j}(x) and s_{10,i, j}(x) ∈ ∑ should be both corrected as positive definite polynomials s_{9,i, j}(x) and s_{10,i, j}(x) ∈ ∑ or nonzero polynomials s_{9,i, j}(x) and s_{10,i, j}(x) ∈ ∑ with degree 0 (ie, positive constant polynomials s_{9,i, j}(x) and s_{10,i, j}(x) ∈ ∑). Based on the aforementioned corrections, we can partially reobtain results for the case d = 2 in Example 1 by using nonzero polynomials s_{9,i, j}(x) and s_{10,i, j}(x) ∈ ∑ with degree 0 as follows: Algorithm 2 returns an inner estimate D₍₂₎ ^M after iterating 13 steps within 220.357 seconds, whose boundary is depicted by red color in Figure; Algorithm 3 returns an inner estimate D₍₂₎ ^BM after iterating 2 steps within 326.797 seconds, whose boundary is depicted by blue color in Figure. (Figure presented.) Black curve, ∂D₀ obtained by; Green curve, ∂D₍₂₎ ^C, Red curve, ∂D₍₂₎ ^C; Blue curve, ∂D₍₂₎ ^BM [Colour figure can be viewed at wileyonlinelibrary.com] Note that, in the original paper, except the case d = 2 in Example 1, s_{9,i, j}(x) and s_{10,i, j}(x) were both preassumed to be nonzero polynomials in ∑ with degree 0 for all other examples when applying SOSTOOLS for implementation. Additionally, since SS_i,j ⊂ S_i,j the transformations for constraints (6) and (7) in both Sections 4.1 and 5.2 are all underapproximative instead of equivalent. Finally, the authors deeply thank Mr Torbjørn Cunis for comments on the mistake caused by s_{9,i, j}(x) and s_{10,i, j}(x) ∈ ∑. The authors also apologize for the mistakes.