Journal ArticleDOI
Descriptor variable systems and optimal state regulation
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In this article, the authors considered linear systems of the form E\dot{x} = Ax + Bu with E singular and proved that the optimal control can be found by solving a reduced order Riccati equation.Abstract:
Linear systems of the form E\dot{x} = Ax + Bu with E singular are treated. It is desired to find a control which drives the system asymptotically to the origin, minimizing a quadratic cost functional. No restrictions are placed on initial conditions. The cost associated with the impulsive behavior of the system is examined as well as existence and uniqueness of the optimal control. Through a sequence of coordinate transformations it is proven that the optimal control can be found by solving a reduced order Riccati equation.read more
Citations
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Journal ArticleDOI
A survey of linear singular systems
TL;DR: In this paper, a brief historical review of linear singular systems is presented, followed by a survey of results on their solution and properties, and the frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.
Journal ArticleDOI
H ∞ control for descriptor systems: a matrix inequalities approach
TL;DR: It is shown that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed H ∞ norm condition as well as stabilizing the closed-loop system and eliminating all impulsive modes.
Journal ArticleDOI
Controllability, observability, and duality in singular systems
TL;DR: In this paper, the concepts of controllability and observability for systems of the form E\dot{x} = Ax + Bu, y = Cx, E singular are considered.
Journal ArticleDOI
Singular perturbations and time-scale methods in control theory: Survey 1976-1983
TL;DR: The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design.
Journal ArticleDOI
The linear-quadratic optimal regulator for descriptor systems
Douglas J Bender,Alan J. Laub +1 more
TL;DR: This paper solves a general finite-horizon problem by applying the calculus of variations to derive the optimal trajectory of the vector consisting of the concatenated descriptor, codescriptor, and control vectors, and calculates the optimal feedback gain relating the control and descriptor variable.
References
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Contributions to the theory of optimal control
TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
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A generalized state-space for singular systems
TL;DR: In this article, a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed, and concepts of controllability and observability are defined for the impulsive modes.
Journal ArticleDOI
Dynamic equations in descriptor form
TL;DR: In this article, the authors studied a general form of sets of equations that is often the product of problem formulation in large-scale systems, especially when the equations are expressed in terms of the natural describing variables of the system.
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Solvability, controllability, and observability of continuous descriptor systems
E. Yip,Richard F. Sincovec +1 more
TL;DR: First, the classical theories of matrix pencils are related to the solvability of descriptor systems, and the concepts of reachability, controllability, and observability of state variable systems to descriptor systems are extended.
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Structural properties of linear dynamical systems
TL;DR: In this article, it was shown that infinite decoupling zeros can be defined, and these induce a fourfold decomposition, of that part of the system giving rise to the polynomial port of the transfer function matrix, analogous to Kalman'B canonical decomposition.