Static State Feedback Law Research Articles

Robust Output Dynamic Min-Max Control for Discrete Uncertain Systems

Min-max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min-max control is a static state feedback law. Recently, the applicability conditions of the discrete static min-max control through the output, have been derived. In this paper, the results for the output static min-max control are further extended to a class of output dynamic min-max controllers, and a general parametrization of all such controllers is derived. The dynamic output min-max control is shown to exist in many circumstances in which the output static min-max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min-max controllers - constructed from an asymptotic observer which is insensitive to uncertainties and a state min-max control - is derived, and shown to have the same stability properties as that of the full state feedback min-max control.

Static-state feedback laws for output regulation of non-linear systems

In this paper static-state feedback laws are considered which address the problem of output stabilization of non-linear dynamic control systems without drift. It is shown that as long as a dynamic-state control law exists which input-output decouples a given system, it is possible to construct a static-state control which stabilizes the system's output. The design procedure sheds light on the inherent difficulties in designing internally stable control laws for non-linear systems. To demonstrate the theory, it is applied to the task of designing an output stabilizing feedback for a simple model of a mobile robot.

Input-output decoupling for linear systems with nonlinear uncertain structure

In this paper the problem of input-output decoupling for linear systems with nonlinear uncertain structure, via an independent of the uncertainties static state feedback law, is studied and solved for the first time. The necessary and sufficient conditions for the problem to have a solution are established. The general analytical expressions of the feedback matrices and the decoupled closed loop system are derived. The decoupled closed loop system structural properties of pole assignment, stabilizability are also studied. All above results are successfully applied to control the longitudinal motion of an aircraft.

Feedback control of two-time-scale nonlinear systems

This article concerns a class of two-time-scale single-input single-output nonlinear systems. For such systems, combination of singular perturbation and geometric methods is employed to synthesize well-conditioned static state feedback laws that induce a well-characterized input-output behaviour and guarantee stability of the closed-loop system. The developed control laws are applied to two nonlinear chemical processes with time-scale multiplicity and their performance is evaluated through simulations.

Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks

It is known that a linear time-invariant system subject to “input saturation” can be globally asymptotically stabilized if it has no eigenvalues with positive real parts. It is also shown by Fuller (1997) and Sussmann and Yang (1991) that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws. In this paper we show the existence of linear state feedback and/or output feedback control laws for semi-global exponential stabilization rather than global asymptotic stabilization of such systems. We explicitly construct linear static state feedback laws and/or linear dynamic output feedback laws that semi-globally exponentially stabilize the given system. Our results complement the “negative result” of Fuller (1977) and Sussmann and Yang (1991).

Design of a minimal precompensator for the decoupling problem

For right invertible linear time-invariant systems, which cannot be decoupled row by row using regular static state feedback laws, we propose a new algorithmic procedure for designing a minimal precompensator leading to a compensated system which can be decoupled by regular static state feedback.

The Regular Local Noninteracting Control Problem for Nonlinear Control Systems

We study the Noninteracting Control Problem for affine nonlinear control systems under the assumption that the number of scalar inputs equals the number of vector outputs. Our purpose is to find a static state feedback law for the system which achieves noninteraction. Using the recently developed differential geometric approach to nonlinear systems theory and working under a set of regularity assumptions, we give necessary and sufficient conditions for the local solvability of the problem. This work extends earlier results in the “geometric approach” for linear systems.

On the structure at infinity of linear block-decouplable systems: The general case

The aim of this note is to show that a linear system ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C, A, B</tex> ) is block-decouplable by means of static state feedback laws ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F, G</tex> ) with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> invertible if and only if the infinite structure of ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C, A, B</tex> ) equals the union of the infinite structures of the subsystems ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{i}, A, B</tex> ) extracted from the given output partition. This result generalizes the ones recently obtained for Morgan's problem [6] and for the particular cases of right-invertible [7] or left-invertibie [8] systems.