Disturbance decoupling by measurement feedback for SISO nonlinearsystems

The measurement feedback disturbance decoupling problem of nonlinear systems with single-input/single-output and single measurement is considered in this paper. Necessary and sufficient conditions are given for disturbance decoupling by static measurement feedback. New necessary conditions and sufficient conditions are presented for disturbance decoupling by dynamic measurement feedback     

Disturbance decoupling for a class of nonlinear MIMO systems by static measurement feedback

In this paper, the disturbance decoupling problem for a square-invertible nonlinear system is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback. The results are valid for left-invertible systems as well.     

Block decoupling of non-linear systems by static measurement feedback

In this paper, the block input-output decoupling problem for non-linear systems is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback.     

Disturbance decoupling and output stabilization by measurement feedback: a combined approach

A very general control problem is solved in the context of the geometric approach to linear multivariable control theory. The problem to be considered is general in the sense that it contains as a special case not only the well-known disturbance decoupling problem by measurement feedback (Schumacher 1981) and the problem of stabilizing the output with respect to disturbances by means of state feedback (Hautus 1970), but also, for instance, the extension of the latter problem to the situation in which only the use of measurement feedback is allowed. Furthermore, connections with and extensions of recent work by Trentelman ( 1986) are given and fruitful use is made of a synthesis of concepts arising from the geometric and the frequency domain approaches to control theory.     

一类MIMO非线性系统的稳定干扰解耦控制

基于非线性系统的微分几何理论相对阶概念,研究了一类M IMO非线性系统的干扰解耦问题(DDP),定义了M IMO系统关于干扰的向量相对阶,给出了该类非线性系统通过静态状态反馈的干扰解耦可解的充分必要条件,并进一步讨论了解耦系统反馈镇定问题,给出了解耦系统可镇定的充分条件,仿真结果验证了该方法的有效性.     

Disturbance decoupling for time delay systems

In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input and the disturbance of the corresponding time delay systems. A stability study using some results due to Pontryagin is presented for the resultant closed-loop system when the delay system is linear. Also, an approximate causal solution is proposed for the nonlinear time delay system based on its linearization around an equilibrium point. © 1997 by John Wiley & Sons, Ltd.     

Diagonal decoupling of linear multivariable systems with constant gain measurement feedback

This note derives a necessary and sufficient condition to diagonally decouple a linear multivariable system through constant gain measurement feedback. This condition is represented in terms of the controllability subspaces and the kernel of a measurement matrix. The number of assignable poles of the resulting closed-loop system is given.     

Input–output decoupling of nonlinear systems by static measurement feedback

This paper gives necessary and sufficient conditions for solvability of the strong input–output decoupling problem by static measurement feedback for nonlinear control systems.     

Disturbance decoupling problems via dynamic output feedback

This paper considers the disturbance decoupling problems, with or without internal stability and pole placement, via dynamic output feedback using polynomial and rational matrix techniques. We show that in all three problems considered, the central solvability condition can be expressed as a two-sided matching problemA = BXC, whereA, B, andCare the polynomial system matrices of certain natural subsystems of the system model andXis to be determined over various subrings of the rational functions. This matching problem can in turn be reduced to certain appropriate zero-cancellation conditions on the polynomial system matricesA, B, andC.     

Input-output decoupling with stability for Hamiltonian systems

The input-output decoupling problem with stability for Hamiltonian systems is treated using decoupling feedbacks, all of which make the system maximally unobservable. Using the fact that the dynamics of the maximal unobservable subsystem are again Hamiltonian, an easily checked condition for input-output decoupling with (critical) stability is deduced.     

Disturbance decoupling and robustness of stability

The problem of finding a feedback compensator to cancel the effect of disturbances on the system output is known as disturbance decoupling. In this paper we investigate the interaction of disturbance decoupling requirement with the robustness of closed‐loop stability in the sense of normalized coprime factor perturbations. This disturbance decoupling and the robust stabilization requirements are expressed in terms of the subspace‐valued functions associated with the plant and the controller and an upper bound on robustness of stability imposed by the disturbance decoupling requirement is derived. This is then compared with the actual robustness of stability that can be achieved by a solution of the disturbance decoupling problem under some simplifying assumptions. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical aspects of disturbance decoupling by measurement feedback

A numerically stable algorithm is given to determine orthogonal similarity transformations such that the system attains a certain condensed form. Using this condensed form, solvability of disturbance decoupling by measurement can be decided by inspection, and controllers can be computed by solving linear equations.     

Disturbance decoupling of switched linear systems

In this paper, we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version, the exogenous input is considered as the disturbance, in the second, the switching signal and in the third both of them are considered as disturbances. All three versions of disturbance decoupling have direct counterparts for linear parameter-varying (LPV) systems, while the latter instance of the problem is relevant for disturbance decoupling of piecewise linear systems, as we will show. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.     

Disturbance attenuation by dynamic output feedback for input-delay systems

This paper addresses the optimal disturbance attenuation problem by output feedback for multivariable linear systems with delayed inputs. The attenuation is optimal in the sense that the controller minimizes the maximal amplitude of the plant output in response to such a disturbance. The controller is a general feedback, involving an observer, a state predictor, and a predicted state feedback. The optimal disturbance attenuation problem is formulated in terms of an equivalent system without delay. The optimal bound of the disturbance attenuation is then characterized, and it is shown that the optimal controller tends to have high gains. A necessary and sufficient condition to guarantee the existence of an optimal solution is provided using the geometric approach.     

-output feedback of infinite-dimensional systems via approximation

As in the finite-dimensional case, a state-space based controller for the infinite-dimensional disturbance-attenuation problem may be calculated by solving two Riccati equations. These operator Riccati equations can rarely be solved exactly. We approximate the original infinite-dimensional system by a sequence of finite-dimensional systems. The solutions to the corresponding finite-dimensional Riccati equations are shown to converge to the solution of the infinite-dimensional Riccati equations. Furthermore, the corresponding finite-dimensional controllers yield performance arbitrarily close to that obtained with the infinite-dimensional controller.     

Disturbance decoupling of linear time-varying singular systems

The problem of disturbance decoupling by state feedback is defined for a linear time-varying singular system. It is required that the closed-loop system has a unique impulse-free solution and its output is not affected by disturbances. An algorithm, namely disturbance decoupling algorithm, is proposed. It is proved that the feasibility of the disturbance decoupling algorithm is invariant under any regular feedback control law. Based on the disturbance algorithm, a constructive method is provided to design a disturbance decoupling feedback control law. Sufficient conditions for the solvability of the disturbance decoupling problem are derived. It is proved that one of the sufficient conditions is also necessary provided that other conditions are satisfied     

Output feedback decoupling of multivariable systems

Necessary and sufficient conditions for output feedback decoupilng of linear time-invariant multivariable systems into single input-multioutput subsystems are derived in frequency domain. The conditions imply a new constructive method for determining a constant gain output feedback matrix and some of its elements can be freely chosen to reassign the closed-loop poles.     

Equivalence of input-output stability and exponential stability for infinite-dimensional systems

For a wide class of infinite-dimensional linear systems it is shown that if the state-space realization is exponentially stabilizable and detectable then exponential stability is equivalent to input-output stability of the transfer function. Exponential stabilizability (or detectability) is a strong assumption as it implies that the system operator satisfies the spectrum decomposition assumption and has finitely many unstable eigenvalues of finite multiplicity. In addition, the finite-dimensional unstable projection of the system is controllable (or observable).     

Proportional-plus-multiintegral stabilizing compensators for aclass of MIMO feedback systems with infinite-dimensional plants

A method is presented for designing proportional-plus-multiintegral stabilizing compensators for a class of feedback systems with exponentially stable infinite-dimensional plants. These compensators enable the feedback system to asymptotically track polynomial inputs and suppress polynomial disturbances of corresponding order. When used in design, the effectiveness of the construction procedure presented can be increased considerably by combining it with the computational stability criterion and semiinfinite optimization. In this manner, the coefficient matrices of a compensator designed by the method can be further modified to ensure better feedback-system performance with respect to various performance requirements, without destroying stability, tracking, and disturbance-rejection properties