Output feedback uniform decoupling problem of linear time-varying analytic systems

A new approach to the input-output uniform decoupling problem of linear time-varying analytic systems via proportional (static) output feedback is introduced. A major feature of the proposed approach is that it reduces the solution of the uniform decoupling problem to that of solving a linear algebraic system of equations, This system of equations greatly facilitates the solution of the three major aspects of the decoupling problem: the necessary and sufficient conditions; the general analytical expressions for the controller matrices; and the structure of the uniformly decoupled closed-loop system.     

Uniform disturbance localization with simultaneous uniform decoupling for linear time-varying analytic systems

The problem of uniform disturbance localization with simultaneous uniform decoupling for linear time-varying analytic systems via static state feedback is investigated, for the first time. The approach presented has the main feature that it reduces the problem to that of solving a homogeneous algebraic system of equations. On the basis of this basic system of equations, the following aspects of the problem are resolved: the necessary and sufficient solvability conditions, the general analytical expressions of all admissible controllers and the morphological characteristics of the closed-loop system     

Uniform exact model matching for a class of linear time-varying analytic systems

The problem of uniform exact model matching is studied via state and output feedback, for a class of linear time-varying analytic systems. The following two major issues are resolved: The nessecary and sufficient conditions for the problems to have a solution and the general analytical expressions for the controller matrices. A major feature of the proposed approach, is that it reduces the uniform exact model matching problem to that of solving a linear nonhomogeneous algebraic matrix equation.     

Minimal-order compensators for decoupling and arbitrary pole placement in linear multivariable systems

Linear multivariable systems that can be decoupled by state-variable feedback are considered. The problem of arbitrary pole placement and/or decoupling by means of output feedback via a dynamic compensator is first obtained through algebraic decoupling theory, Then an optimization problem in the free compensator parameters is derived by defining a performance index that measures both the amount of coupling in the closed-loop system and, when pole placement is also desired, the error in the closed-loop pole locations. The theory necessary for solving this optimization problem by means of standard gradient algorithms is developed. Minimal-order solutions are obtained because the compensator structure considered is quite general. Two illustrative numerical examples are presented.     

Partial model matching via static feedback (the multivariable case)

The problem of partial model matching is studied for the case of multi-input/multi-output (MIMO) linear time-invariant systems. Using a regular static state feedback law, the necessary and sufficient conditions for the problem to have a solution are established, the general analytic expressions of the controller matrices are derived. For the case of single-input/single-output systems sufficient conditions are derived for the solution of the partial model matching problem with simultaneous stabilizability. For the same type of systems the necessary and sufficient conditions for the solution of the partial model matching problem with simultaneous regulation of the free response of the closed loop system are established. Finally, the problem of partial model matching, via regular static measurement output feedback, is solved for the case of MIMO systems     

Disturbance decoupling in a class of linear systems

The disturbance decoupling problem by state feedback (DDP) is solved for a class of linear systems where the left-invertible systems are included. Also obtained is a complete characterization of the solution as well as the parameterization of all corresponding state feedback matrices. Such characterization enables one to conclude about the solvability of DDP with stability and/or pole placement. A numerical method is proposed for computation of the controllers in an analytical form, suitable to the treatment of complementary design specifications. The solution of the disturbance decoupling problem by measurement feedback (DDPM) is also discussed and, based on the results obtained for DDP, a procedure for design of a reduced-order compensator is proposed     

Transfer matrix approach to the triangular block decoupling problem

The triangular block decoupling problem for linear multivariable systems is studied via the transfer matrix approach. This approach clearly separates the problem of admissible control laws from the one of desired decoupled system specifications. Necessary and sufficient triangular decoupling conditions are given for various control laws. These conditions are expressed in a very simple way in terms of linear dependance among the transfer matrix rows. It turns out that when the problem is solvable, this can be done by static state feedback on a minimal realization of the system. Furthermore it is shown that whenever triangular block decoupling is possible, it is also attainable with stability.     

Noninteracting control of 2-D systems

Necessary and sufficient conditions for the existence of a decoupling bicausal precompensator for multivariable 2-D systems are derived in state-space and frequency domains. In general, the decoupling problem for 2-D systems can be solved by feedback compensators if suitable injectivity assumptions are introduced on the input-state matrices. The structure of dynamic compensators is derived for this case, and the 2-D decoupling problem with stability is solved     

Disturbance decoupling control design for switched Boolean control networks

This paper investigates a kind of disturbance decoupling problems (DDPs) for switched Boolean control networks (BCNs), that is, the disturbance-independent output decoupling problem, via the semi-tensor product of matrices. By converting the dynamics of switched BCNs into an algebraic form and using the redundant variable separation technique, all possible state feedback controllers are designed for the disturbance-independent output decoupling problem. Then, based on the obtained state feedback disturbance decoupling controllers and the system’s output equation, a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers. The study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched BCNs.     

A parametric frequency domain approach to decoupling with coupled rows

This contribution considers the incomplete decoupling of non-minimum phase and non-decouplable systems by static state feedback, where a stable diagonal decoupling is not possible. By introducing a coupled row in the reference transfer matrix, so that one output is affected by several reference inputs, an incompletely decoupled but internally stable closed loop system is obtained. This decoupling problem is solved using a parametric approach to the design of state feedback controllers in the frequency domain. Explicit expressions are derived for the design parameters of the state feedback controller achieving the decoupled reference transfer matrix. A simple example demonstrates the proposed design procedure.     

Robust triangular decoupling with simultaneous robust disturbance rejection

For the case of a linear time invariant system with nonlinear uncertain structure the problem of robust triangular decoupling with simultaneous robust disturbance rejection (RTDRDR) is studied. The necessary and sufficient conditions for the solution of the RTDRDR problem are established. The general expressions for the feedback matrices solving the problem are derived in analytic form. The resulting closed-loop system, being triangularly decoupled and having no influence from the disturbances to the output, is analytically determined. For the solution of the RTDRDR problem with simultaneous robust stability, sufficient conditions are established. The present results are successfully applied to control a vertical take-off and landing aircraft in hover.     

状态反馈预测控制干扰解耦的研究

讨论状态反馈预测控制系统设计中的干扰解耦设计问题，给出了状态反馈预测控制系统干扰可解耦设计的充分必要条件。基于状态空间模型，给出了状态反馈预测控制系统设计参数——预测时域按干扰解耦设计的选取方法。它可改善控制系统的性能，提高控制系统的抗干扰能力。仿真结果表明了状态反馈预测控制系统干扰解耦设计的有效性。     

Parameterization of decoupling control laws for affine nonlinearsystems

The problem of parameterizing all the decoupling feedbacks is investigated and applied to the design of a stable noninteracting control for affine nonlinear systems. An algebraic study of controlled invariance is presented. It covers a new criterion for controlled invariance, parameterization and novel properties of the friend set, and computational aspects of the maximal controlled invariant distribution. This analysis is used to derive Falb-Wolovich-like conditions for general decoupling (including disturbance decoupling and noninteracting control) problems. It is shown that to determine all the decoupling feedbacks one usually needs infinitely many (sets of) controlled invariant or controllability distributions that can arise as solutions to the problems. It is also shown that under certain conditions, stable noninteracting design based on first parameterizing the decoupling feedbacks is still a feasible approach in the sense that a feedback can be chosen from the friend set of the maximal solution for the exponentially stable and noninteracting design problem     

Input-output block decoupling of linear time-varying singularsystems

The input-output block decoupling problem by state feedback is studied for linear time-varying singular systems. First, an algorithm, the regularization algorithm, is developed such that the system can be made by state feedback to have a unique impulse-free solution. Second, another algorithm, the block decoupling algorithm, is proposed, which provides sufficient conditions for the solvability of the input-output block decoupling problem. Then, a decoupling feedback law is constructed such that the corresponding closed-loop system is regular, impulse-free, and noninteractive. Finally, an example is given to illustrate the applicability of the algorithms     

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 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.     

模糊关系系统的反馈解耦

本文研究动态模糊关系系统的输出反馈解耦问题.在给定的开环系统表述形式下,提出 了一种解耦控制器的结构,并导出了若干涉及解耦问题的解的结论.     

Generalized controlled invariance for discrete-time nonlinearsystems with an application to the dynamic disturbance decouplingproblem

In analogy with the continuous-time case, a general notion of controlled invariance with respect to quasi-static-state feedback is introduced for discrete-time nonlinear systems which incorporates the earlier definition of controlled invariance with respect to regular static-state feedback. This new notion is used to derive a geometric solution to the dynamic disturbance decoupling problem. The proposed solution is a natural generalization of the geometric solution to the static disturbance decoupling problem     

Disturbance localization for left invertible linear periodic discrete-time systems

The disturbance localization problem for left invertible linear periodic discrete-time systems is solved using periodic state feedback controllers. The proposed technique is of algebraic nature and has the following two main characteristics: (i) It yields simple algebraic criteria for testing the solvability of the problem, as compared to known geometric criteria, which may not be so easy to check. (ii) It derives analytically the general expressions of all periodic controllers admissible for disturbance localization, as compared to known techniques, which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures. Moreover, for the aforementioned class of periodic systems, the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated, and conditions for its solvability are established, on the basis of a decentralized control approach, that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback.     

Decoupling by dynamic measurement feedback with stability:necessary and sufficient conditions

The noninteracting control problem of linear time-invariant multivariable systems by dynamic measurement feedback is solved in the state-space geometric approach. The generalization of W.M. Wonham's EDP (1979) is considered. The problem of the reduction of compensator's order is not treated, but the solution derived is able to solve simultaneous problems like the decoupling and the disturbance decoupling problems