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.     

Input–output feedback linearization for nonminimum phase nonlinear systems through periodic use of synthetic outputs

Input–output feedback linearization provides a convenient means of extending linear control strategies such as output zeroing or pole placement to the case of nonlinear affine in the input systems, but such extensions cannot be applied in the presence of nonminimum phase characteristics. This paper overcomes this difficulty through the periodic use of a finite number of synthetic outputs which are so constructed as to define embedded dynamics with stable zero dynamics. The efficacy of the method is demonstrated by means of a numerical example.     

Robust static output feedback design for polynomial nonlinear systems

A computational scheme of solving the nonlinear static output feedback design problems for a class of polynomial nonlinear systems is investigated in this paper. Sufficient conditions to achieve the closed‐loop stability with or without H_∞ performance are presented as state‐dependent matrix inequalities, which provides an effective way for the application of the new sum of squares programming technique to obtain computationally tractable solutions. By introducing additional matrix variables, we succeed in eliminating the coupling between system matrices and the Lyapunov matrix. The proposed methodology is also extended to the synthesis for the parameter‐dependent polynomial systems. Robust polynomial output feedback controller is designed in an efficient computational manner. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed methodology. Copyright © 2009 John Wiley & Sons, Ltd.     

Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem.     

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.     

Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback

This paper proposes a systematic approach for the static output feedback control design for discrete-time uncertain linear systems. It is shown that if the open-loop system satisfies some particular structural conditions and the uncertainty has a specific structure, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and nonsquare systems are considered. The performance problem through a quadratic criterion is also discussed (guaranteed cost control).     

Almost disturbance decoupling for a class of nonlinear systems via sampled‐data output feedback control

This paper addresses the problem of almost disturbance decoupling (ADD) using sampled‐data output feedback control for a class of continuous‐time nonlinear systems. Under a lower‐triangular linear growth condition, a sampled‐data output feedback controller is constructed based on the output feedback domination approach, and a Gronwall–Bellman‐like inequality is established in the presence of disturbances. Even though a sampled‐data controller is employed for easy computer implementation, the proposed controller is still able to achieve ADD under the commonly used continuous‐time requirement, that is, the disturbances' effect on the output is attenuated to an arbitrary degree of accuracy in the L₂ gain sense. Copyright © 2015 John Wiley & Sons, Ltd.     

LQG optimal scalar static output feedback

An eigenproblem-based technique is given for computing the stabilizing scalar static output feedback gain that minimizes the standard linear quadratic performance index in the presence of a Gaussian white-noise disturbance. The method adapts recent work on eigenproblem-based computation of _∞-norms.     

Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback

In this paper, a class of nonlinear interconnected systems with nonlinear nominal subsystems is considered. Matched and mismatched uncertainties are both dealt with. Based on sliding mode techniques, a decentralised robust control scheme, using only output information, is presented to stabilise the system locally, but under certain circumstances, global results can be obtained. The approach allows a more general structure for the interconnections and uncertainty bounds than other literature in this area. The conservatism in the results is reduced by fully using system output information and the uncertainty bounds. A numerical example is used to demonstrate the efficacy of the method.     

Decentralised memory static output feedback control for the nonlinear time-delay similar interconnected systems

In this paper, the problem of decentralised memory static output feedback control for a class of nonlinear time-delayed interconnected systems with similar structure is investigated, where both the linear and nonlinear state vectors involve time delay. The contributions of the paper include the following: (1) a new similar structure is presented via memory static output feedback; (2) by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised memory static output derivative feedback controllers with similar structure are designed, which is dependent of time delays, to stabilise the interconnected systems uniformly asymptotically; and (3) the stability domain is estimated. The conservatism of the results obtained is reduced by full using the system output information. Finally, the numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.     

Global stabilization of uncertain stochastic nonlinear time‐delay systems by output feedback

Constructive control techniques have been proposed for controlling strict feedback (lower triangular form) stochastic nonlinear systems with a time‐varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. The delay‐independent output feedback controller making the closed‐loop system globally asymptotically stable is explicitly constructed by using a linear dynamic high‐gain observer in combination with a linear dynamic high‐gain controller. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust adaptive tracking of uncertain nonlinear systems by output feedback

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high‐gain scaling technique and a new adaptive law, a linear‐like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Global output feedback stabilisation of nonlinear time-delay systems with unknown output function

This paper studies the problem of global output feedback stabilisation for a class of nonlinear time-delay systems with the unknown output function. By constructing the appropriate Lyapunov–Krasovskii functional and observer, skillfully combining generalised adding a power integrator technique, sign function and homogeneous domination approach, an output feedback controller is designed to guarantee globally uniformly asymptotical stability of nonlinear time-delay systems with the unknown output function.     

Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty

Even in the presence of uncertainty in both state and output equations, we prove that global asymptotic stabilization is still possible by output feedback for a family of uncertain nonlinear systems dominated by a triangular system with a polynomial output‐dependent growth rate. In contrast to the linear growth requirement in the recent work the nonlinear perturbations in this paper are allowed to satisfy a linear growth condition with a polynomial output‐dependent rate. To handle simultaneously the polynomial nonlinearities and unknown parameter in the system output, we propose a high‐gain estimator with a dynamic gain that is updated online through a Riccati‐type dynamic equation. Then, an estimator‐based controller is designed by a recursive algorithm that makes it possible to assign the controller gains step by step. The globally stabilizing output‐feedback controller developed in this paper is robust with respect to uncertainties in the system dynamics and output equations.     

The H∞ control problem using static output feedback

In this paper we shall consider the H_∞ control problem using static output feedback. The approach uses some recent results from linear algebra. The main result shows that the H_∞ control problem is solvable by a static output feedback controller if and only if there exists a positive definite matrix satisfying two certain quadratic matrix inequalities. A parametrization of all static output feedback H_∞ controllers is given.