Design and Implementation of a DC-DC Converter Based on Variable Structure Control of Switched Systems*

Robust switched control based on strictly positive real systems and variable structure control techniques

“…This paper shows that there exists a solution of the SPR synthesis for a class of linear uncertain switched systems using switched static output feedback, if and only if there exists a solution of this SPR synthesis with switched static state feedback. This result is a generalization of known conditions regarding this problem , for linear time invariant and known (without uncertainties) plants and offers a possible procedure for output feedback SPR synthesis: first solve the state feedback SPR synthesis, and then, using the obtained solution, find a solution for the output feedback SPR. Defining n , m , and p as the numbers of state variables, inputs, and outputs of the uncertain switched plant, respectively, are presented necessary and sufficient conditions for the switched static state feedback (Theorem ) and for the switched static output feedback necessary and sufficient conditions when p = m , and sufficient conditions when m < p < n (Theorems and ).…”

“…The next theorem is a generalization of the results presented for linear time invariant and known plants in , now for a class of uncertain switched plants. First, consider an important performance index, called the decay rate.…”

“…Finally, and are equivalent and follows from the condition M i q = K i q C i X i . □Remark The condition presented in Theorem solves Problem and generalizes to a class of uncertain switched systems the method proposed in for known linear time‐invariant plants. Thus, this result can be useful in the design of switched static state feedback controllers for uncertain switched plants, based on SPR synthesis (see Section 4.2 for more details).Remark Observe that in Problems and , α defined in is an uncertain vector.…”

“…Based on the control techniques and definitions presented in Section 2, in were proposed new results about SPR synthesis of a class of known linear switched systems expressed through the so‐called LM‐SPR, introduced in . Based on these results, the proposed methods in this paper are an extension of the aforementioned results, now for a class of uncertain linear switched systems.…”

“…The proposed method in this paper is based on the methods presented in , where the same problem is solved, but with the advantage of engaging the robust control design, and thus can be applied in the control of uncertain switched systems with higher efficiency. As far as we know, the proposed formulation was not yet applied in the control design of uncertain switched systems, and through the results of an example analyzed, one can verify the effectiveness of the proposed method.…”