Shifting linear quadratic control of constrained continuous-time descriptor LPV systems*

Recently, the concept of shifting linear quadratic control (SLQC), where some varying parameters are introduced and used to schedule the weighting matrices of a quadratic cost function, has been introduced. This paper further explores this concept by considering the presence of constraints in the system to be controlled. In particular, two types of constraints are considered: a) algebraic constraints between the variables of the system; and b) constraints on the allowed values for the input and the state variables. The proposed solution, investigated under the descriptor linear parameter varying (D-LPV) framework, requires solving a set of linear matrix inequalities (LMIs), a problem for which efficient solvers are available nowadays. A numerical example illustrates the application of the proposed theory.