Physical realizability of output feedback control laws

In this paper we consider linear and nonlinear dynamic systems which are stabilizable via output feedback. In general, e.g. when the output feedback control law is carried out by zero insertion, such feedback is not physically realizable. It is shown that the insertion of some high frequency poles, which play the role of reduced order observer for the estimation of the output time derivatives, guarantees: (i) the physical realizability of the control law, and (ii) the fulfilment of the required stability properties.     

On passivation with dynamic output feedback

This note extends recent results on full-state feedback stabilization of linear-nonlinear cascades to the case when, from the linear part of the cascade, only an output, rather than the state, is available for feedback. Special attention is given to weak minimum phase systems     

Finite-time stabilization via dynamic output feedback

In this paper the finite-time stabilization of continuous-time linear systems is considered; this problem has been previously solved in the state feedback case. In this work the assumption that the state is available for feedback is removed and the output feedback problem is investigated. The main result provided is a sufficient condition for the design of a dynamic output feedback controller which makes the closed loop system finite-time stable. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multi-objective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time stability together with some pole placement requirements.     

Stabilization via dynamic output feedback for systems with output nonlinearities

The problem of asmptotically stabilizing a class of systems by means of continuous output feedback is considered. These systems are characterized by nonlinear terms, depending only on the ouputs. It is shown that for these systems stabilization via continuous state-feedback plus stabilization via output injection imply stabilization via continuous dynamic output-feedback. This generalizes a well-knwon result for linear systems.     

On discrete dynamic output feedback min-max controllers

The paper considers output feedback min-max controllers for non-square discrete time uncertain linear systems. Based on previous work, it is demonstrated that static output feedback min-max controllers are only realizable for a specific class of systems. To broaden this class, a compensator based framework is proposed to introduce additional degrees of freedom. The conditions for the existence of such dynamic output feedback min-max controllers are given and are shown to be relatively mild. Furthermore, a simple parameterization of the available design freedom is proposed. An explicit procedure is described which shows how a Lyapunov matrix, which satisfies both a discrete Riccati inequality and a structural constraint, can be obtained using Linear matrix inequality optimization. This Lyapunov matrix is used to calculate the robustness bounds associated with the closed-loop system. A simple aircraft example is provided to demonstrate the efficacy of the design approach.     

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.     

Pole assignment using dynamic output feedback compensators

The design of dynamic output feedback compensators for the pole assignment of linear time-invariant multivariable systems is considered. A systematic procedure is developed for the synthesis of the transfer function matrix of the compensator. A certain number of poles can be arbitrarily assigned by the proposed compensator. Moreover, in order to assign more poles using a compensator of the same order as before, a new approximate assignment approach based on the least-square-error algorithm is proposed. A numerical example is given to demonstrate the effectiveness of the proposed approaches.     

Decoupling of linear systems by dynamic output feedback

Necessary and sufficient conditions for decoupling of linear systems by dynamic output feedback are derived, under the requirement that the decoupled system be internally stable. The conditions are stated in terms of quantities which are directly related to the transfer matrix of the given system. The main issue is resolved through the introduction of a new concept—the strict adjoint. The strict adjoint is a minimal polynomial matrix that diagonalizes a given matrix.This research was supported in part by US Army Research Grant DAAG29-80-C0050 and US Air Force Grant AFOSR76-3034D through the Center for Mathematical System Theory, University of Florida, Gainesville, Florida 32611, U.S.A.     

Linear dynamic output feedback: Invariants and stability

A full invariant under linear dynamic output feedback is derived. Some of its applications to the design of internally stable feedback control systems are considered.     

Noninteracting control by output feedback and dynamic compensation

The design of noninteracting multivariable control systems by slate feedback has received considerable attention recently, and an extensive theory is now available. One area, however, that requires further clarification concerns the case where the state vector is not accessible to measurement, and feedback of output is inadequate for the purpose of decoupling. In this paper a new technique is described by means of which it is possible to decouple a system which is not olherwise decouplable by proportional feedback of the output vector. The technique is based on the addition of a dynamic controller in the forward path, and is analogous to cascade compensation in single-loop systems. It is shown that a necessary and sufficient condition for the success of this method of decoupling control is that the Original system should satisfy the condition for state feedback decoupling.     

On stabilization of decentralized dynamic output feedback systems

A dynamic output feedback law is presented for large scale interconnected systems. If the coupling terms between the subsystems are neglected, the control scheme can be interpreted as decentralized reconstruction of the state variables from the output of the subsystems. A class of systems stabilizable by decentralized state feedback is investigated. A sufficient condition is determined for systems to be stabilizable with local state feedback and reconstruction with observers of full order. The resulting closed-loop systems are connectively stable. Moreover, any prescribed degree of stability can be achieved and the closed-loop systems are robust with respect to bounded nonlinearities in the couplings between the subsystems.     

Cooperative linear output regulation for networked systems by dynamic measurement output feedback

This paper investigates the cooperative linear output regulation problem of a class of heterogeneous networked systems with a common reference input but with different disturbances for individual nodes. A novel distributed control law is presented based on dynamic measurement output feedback. It is shown that the overall networked closed-loop control system is asymptotically stable and the output regulation errors asymptotically approach zero as time goes to infinity under a sufficient and necessary condition. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control law.     

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.     

Exact pole assignment using direct or dynamic output feedback

This note addresses the problem of the assignability of the eigenvalues of the matrixA + BPCby choice of the matrixP. This mathematical problem corresponds to pole assignment in the direct output feedback control problem, and by proper changes of variables it also represents the pole assignment problem with dynamic feedback controllers. The key to our solution is the introduction of the new concept of local complete assignability which in loose terms is the arbitrary perturbability, of the eigenvalues ofA + BPCby perturbations ofP. If nxis the order of the system, we show that ifA + BP_{0}Chas distinct eigenvalues, a necessary and sufficient condition for local complete assignability at P0is that the matricesC[A + BP_{0}C]^{i-1}Bbe linearly independent, for1 leq i leq n_{x}. In special cases, this condition reduces to known criteria for controllability and observability. Although these latter properties are necessary conditions for assignability, we also address the question of the assignability of uncontrollable or unobservable systems both by direct output feedback and dynamic compensation. The main result of this note yields an algorithm that assigns the closed-loop poles to arbitrarily chosen values in the direct and in the dynamic output feedback control problems.     

基于参数依赖动态输出反馈鲁棒MPC的混沌系统同步

针对离散时间不确定混沌系统的同步控制问题,提出一种基于参数依赖动态输出反馈鲁棒模型预测控制算法.首先,采用主动控制策略,将具有噪声扰动的主从混沌系统同步问题转化为鲁棒稳定性问题;然后,采用参数依赖动态输出控制器和二次有界概念,在保证闭环系统鲁棒稳定性的同时,降低算法的保守性;最后,通过附加约束条件,能够显式处理混沌系统同步中的输入约束.仿真结果表明了所提出算法的有效性.     

On dynamic output feedback compensator design using the Riccatiequation

A simple formula for the design of dynamic output feedback compensators so as to reduce closed-loop system sensitivity is given. It is obtained by reformulating the compensator design problem as a deterministic linear optimal state regulator problem (i.e., an LQG problem), and an appropriate sensitivity reduction interpretation. The result is given for SISO linear systems     

Dyadic output feedback laws generated as Kronecker products : optimal and suboptimal solutions

The problem of eigenvalue assignment in the system dx/dt equals; Ax + Bu, y = Dx, using the dyadic output feedback law u = u₀ + q · p^Ty is considered via a formulation developed earlier by the author, in which p and q occur in the Kronecker product vector p?q. The equations governing the values of p and q which give an optimum approximation to a prescribed spectrum of eigenvalues are derived, and a special case is solved. Various facets of the problem of generating suboptimal solutions are discussed.     

Design of dynamic output feedback controller for power system stabilization

A computational method of designing dynamic compensators for stabilization of power systems is described. The control strategy only employs feedback from the available system output variables. A design procedure which would result in a stable closed-loop system over wide operating points is also included.