Showing papers by "Hassan K. Khalil published in 1989"
TL;DR: In this article, it is shown that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure, where the overall compensator is taken as a parallel or cascade connection of the slow and fast compensators.
Abstract: Feedback control of linear time-invariant singularly perturbed systems of the form x=A/sub 11/x+A/sub 12/z+B/sub 1/u, epsilon z=A/sub 21/x+A/sub 22/z+B/sub 2/u,y=C/sub 1/x+C/sub 2/z Eu, where A/sub 22/ may be singular, is discussed. It is shown that, under stabilizability-detectability assumptions on the slow and fast models, the theory of feedback control of singularly perturbed systems can be extended to the case of singular A/sub 22/. Both state and output feedback results are given. In particular, a parameterization of all compensators that stabilize the system while preserving its two-time-scale structure is given. It is shown that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The overall compensator is taken as a parallel or cascade connection of the slow and fast compensators. The sequential procedure is applied to the design of high-gain feedback compensators for a class of multivariable plants. >
79 citations
21 Jun 1989
TL;DR: In this article, the authors studied feedback control of linear time-invariant singularly perturbed systems of the form? = A 11 x + A 12 z + B 1 u + B 2 u y = C 1 x + C 2 z + Eu where Eu may be singular.
Abstract: This paper studies feedback control of linear time-invariant singularly perturbed systems of the form ? = A 11 x + A 12 z + B 1 u ? = A 21 x + A 22 z + B 2 u y = C 1 x + C 2 z + Eu. where A 22 may be singular. It is shown that, under stabilizability-detectability assumptions on the slow and fast models, the theory of feedback control of singularly perturbed systems can be extended to the case of singular A 22 . Both state and output feedback results are given.
57 citations
TL;DR: In this paper, the robustness of sampled-data control designs to unmodeled high-frequency dynamics is studied using singular perturbation theory, and it is argued that when the plant is preceded by a zero-order hold, a direct transmission term of the reduced-order model should be modeled as a delay element in order to ensure robustness.
Abstract: Robustness of sampled-data control designs to unmodeled high-frequency dynamics is studied using singular perturbation theory. It is argued that when the plant is preceded by a zero-order hold, a direct transmission term of the reduced-order model, which results from neglecting high-frequency dynamics, should be modeled as a delay element in order to ensure robustness. >
40 citations
21 Jun 1989
TL;DR: In this article, the problem of observer design for a class of state-feedback controllers that includes high-gain linear control, continuous approximations of min-max control and variable structure control is studied.
Abstract: In this paper we study the problem of observer design for a class of state-feedback controllers that includes high-gain linear control, continuous approximations of min-max control and continuous approximations of variable structure control. Assuming that the state-feedback controller robustly stabilizes the system in the presence of matched parametric uncertainties, we are to design the observer such that the observer-based control recovers the stability robustness of the state-feedback-control. We will show that it is possible to design such an observer, if the nominal, system is left-invertible and minimum-phase.
37 citations
TL;DR: It is shown that application of the composite control results in a final state that is O(ϵ) close to the desired state, and a value of the cost that isclose to the optimal cost of the reduced problem.
16 citations
TL;DR: In this paper, the authors presented a method for modeling a two-time-scale system in the singularly perturbed form using an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK.
Abstract: A method is presented for modeling a two-time-scale system in the singularly perturbed form. The method uses an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form by a transformation into an ordered real Schur form, followed by balancing. Second, under some conditions on the ordered real Schur decomposition, a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables. >
7 citations
13 Dec 1989
TL;DR: In this paper, an observer-based feedback control for nonlinear systems with left-invertible, minimum-phase, and fully linearizable state feedback is proposed, in which the state feedback component is a robust, possibly nonlinear, stabilizing state-feedback control law.
Abstract: A study is made of the problem of output feedback control of nonlinear systems that are left-invertible, minimum-phase, and fully linearizable (by static state feedback). The proposed control is an observer-based control in which the state feedback component is a robust, possibly nonlinear, stabilizing state-feedback control law. The observer is designed so that the closed loop system is a two-time-scale singularly perturbed system. However, due to the epsilon -dependent scaling of the state variables, some of the standard singular perturbation results do not hold for the closed-loop system, in general. The authors present new singular perturbation results on the behavior of the closed-loop system in the presence of such scaling. In particular, they argue that the undesirable effects of such scaling would not arise if the state-feedback control were globally bounded. >
7 citations