The design of reduced-order controllers is considered for stabilization control, covariance upper bound control, linear quadratic regulator, ∞ control, H∞ control, positive real control problems and robust H2 contro...The design of reduced-order controllers is considered for stabilization control, covariance upper bound control, linear quadratic regulator, ∞ control, H∞ control, positive real control problems and robust H2 control, robust ∞ control and robust H∞ control problems for generalized linear plants without any additional assumptions. An upper bound of the order is obtained with which the (robust) controllers can guarantee stability constraints and satisfy the same design objectives as the so-called 'full-order' controllers. A unified linear-matrix-inequality ( LMI) based approach to reduced-order (robust) controller design for all the above-mentioned problems is provided. It us shown that each of these problems is solvable if and only if two uncoupled LMIs with an LMI-type constraint have a pair of positive definite solutions, one of which has a lower dimension than that given by Skelton and iwasaki (1995). All desired reduced-order (robust) controllers are parameterized via the solutions of LMIs Moreover, a design procedure is proposed based on the above LMI approach.展开更多
This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) probl...This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The design of reduced-order controllers is considered for stabilization control, covariance upper bound control, linear quadratic regulator, ∞ control, H∞ control, positive real control problems and robust H2 control, robust ∞ control and robust H∞ control problems for generalized linear plants without any additional assumptions. An upper bound of the order is obtained with which the (robust) controllers can guarantee stability constraints and satisfy the same design objectives as the so-called 'full-order' controllers. A unified linear-matrix-inequality ( LMI) based approach to reduced-order (robust) controller design for all the above-mentioned problems is provided. It us shown that each of these problems is solvable if and only if two uncoupled LMIs with an LMI-type constraint have a pair of positive definite solutions, one of which has a lower dimension than that given by Skelton and iwasaki (1995). All desired reduced-order (robust) controllers are parameterized via the solutions of LMIs Moreover, a design procedure is proposed based on the above LMI approach.
基金supported by National Natural Science Foundation of China(Nos.61004017 and 60974103)
文摘This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.
