Abstract
A regulator design method is presented for switched bimodal linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. The switching in the bimodal system is defined by a switching surface. The regulator design approach consists of three steps. The first step is based on constructing a switched observer‐based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics to construct a parameterized set of switched controllers. In the third step, two sufficient regulation conditions are derived for the resulting switched closed loop system. The regulation conditions present guidelines for the selection of the additional dynamics used to parameterize the switched controllers to yield the desired regulator. A regulator synthesis approach is proposed based on solving properly formulated bilinear matrix inequalities. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.
Highlights
Switched control systems have attracted much attention in the control community since they present challenging problems of practical importance
The state space representation of the system Jr given in 3.2 differs from that traditionally used in the construction of parameterized sets of stabilizing controllers for linear systems in that the state equation in 3.2 contains the additional term LrDry Drx xQ
The proposed synthesis approach is based on solving a set of properly formulated bilinear matrix inequalities BMIs
Summary
Switched control systems have attracted much attention in the control community since they present challenging problems of practical importance. Solutions to the output regulation problem for the case of linear systems have been presented in 13–15 and for the case of nonlinear systems in 16, These results cannot be applied to switched systems since the vector fields of switched systems are discontinuous and nonsmooth. A controller design approach is proposed for single-input single-output switched bimodal systems, where it is desired to reject known disturbance signals and track known reference inputs simultaneously. Two sufficient regulation conditions are derived for the switched closed loop system. The first sufficient condition is derived based on the input-output stability property of the switched closed loop system. The second sufficient condition for regulation is derived by transforming the forced switched closed loop system into an unforced impulsive switched system. For a given 1 × N matrix X, X denotes the N × 1 vector with the same entries as those of XT
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