Switching control design for LTI system with uncertain equilibrium: Application to parallel interconnection of DC/DC converters

Robust switching control design using Lur'e Lyapunov functions

“…In the continuous context, recall that the global stabilization of the linear system ̇x = Ax + Bu subject to bounded controls is possible if and only if the pair (A, B) is stabilizable and none of the eigenvalues of A has strictly positive real part 37(p. 19) . As a result, for Assumption 3 to hold, it is necessary that, for all 𝜃 ∈ Θ, no eigenvalue of A(𝜃) has strictly positive real part, since the spectrum 𝜎( Ā(𝜃)) of Ā(𝜃) equals 𝜎(A(𝜃)) ∪ {0}, see (33).…”

“…To the best of our knowledge, Reference 33 is the only paper that proposes a robust control law design embedding an internal model, in the context of switched systems. Unlike previously cited papers, (H) is not required, robustness is ensured a priori at the stabilizer design step and, finally, LMI‐based design procedure allowing to enlarge an inner estimation of the basin of attraction is proposed.…”

“…Unlike previously cited papers, (H) is not required, robustness is ensured a priori at the stabilizer design step and, finally, LMI‐based design procedure allowing to enlarge an inner estimation of the basin of attraction is proposed. However, the results presented in Reference 33 rely on some restrictive assumptions, namely: (i) the approach is limited to invertible linear systems, which implies that the number of inputs must be equal to number of regulated outputs; (ii) by using quadratic Lyapunov functions, not only achievable closed‐loop stability is merely local but also estimates of the domain of attraction can only be ellipsoidal sets which may be conservative.…”

“…Even without uncertainties, this is a non trivial task due to the fact that (H) does not hold for the augmented switched dynamics. In contrast with existing results, a design procedure handling robustness a priori is proposed in Reference 33. Its applicability is limited to invertible linear systems and achievable stability is only local, though.…”

“…In this article, we present a methodology that dramatically enlarges the scope of Reference 33 and offers less conservative results. The contributions of this article are threefold.…”