Robust H∞ control for uncertain discrete singular systems with pole placement in a disk

This paper addresses the design of robust H_∞ controllers for uncertain discrete singular systems with time-invariant uncertainty in both the state and measurement matrices. The singular system to be controlled is not assumed to be regular. A regular dynamic output feedback controller is designed such that a prescribed H_∞ performance condition is satisfied and the closed-loop poles are placed in a specified disk while the regularity, causality and stability of the closed-loop system can be guaranteed for all admissible uncertainties. The desired controller can be obtained by solving a set of matrix inequalities. A numerical example is given to demonstrate the application of the proposed method.     

Parameter-insensitive pole assignment

A problem of parameter-insensitive pole assignment for a kind of finite-dimensional linear time-invariant (FDLTI) system is considered. Conditions for the existence of some parameter-insensitive poles are obtained. Further, an approach for constructing the feedback law is suggested.     

Some results on the genericity of the pole placement problem

In this note, the pole placement problem for a linear MIMO systems with p outputs and m inputs is studied from the algebraic point of view. A formulation is proposed, that allows to analyze both theoretical and numerical aspects of the case min(m,p)=2 with more sharpness. Moreover, here it is shown that arbitrary pole placement by static output feedback of unitary rank is generically not possible even if m+p>n holds true.     

Arbitrary pole placement with the extended Kautsky–Nichols–van Dooren parametric form

We consider the classic problem of pole placement by state feedback. The well-known eigenstructure assignment algorithm of Kautsky, Nichols, and van Dooren is extended to obtain a parametric formula for the pole-placing feedback matrix that can deliver any desired closed-loop eigenvalues, with any desired multiplicities.     

A unified method for optimal arbitrary pole placement

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.     

Robust constrained predictive control using comparison model

This paper proposes a quadratic programming (QP) approach to robust model predictive control (MPC) for constrained linear systems having both model uncertainties and bounded disturbances. To this end, we construct an additional comparison model for worst-case analysis based on a robust control Lyapunov function (RCLF) for the unconstrained system (not necessarily an RCLF in the presence of constraints). This comparison model enables us to transform the given robust MPC problem into a nominal one without uncertain terms. Based on a terminal constraint obtained from the comparison model, we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints. Since this terminal condition is described by linear constraints, the control optimization can be reduced to a QP problem.     

Robust stability analysis of time-varying systems using time-varying quadratic forms

We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.     

Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel

The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed.     

预报辨识、映照模型及自校正极点配置鲁棒控制系统

本文以反馈通道存在延时的实际系统为背景,提出了一种简单的参数预报辨识算法,分析证明了该算法的区域收敛性。此外,文中还引入了映照模型的概念,并以此为基础,设计了一种算法简单的自校正极点配置鲁棒控制器,证明了映照模型的跟踪性质和整个闭环系统的稳定性。理论分析及仿真的结果表明,本文给出的方法是可行的。     

A necessary condition for pole assignment by constant output feedback

In this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques. In particular, a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed-loop system to any desired positions.     

Robust pole location with experimental validation for three-phase grid-connected converters

This paper provides design and experimental validation of robust current controllers for three-phase grid-connected converters. The main objectives here are: (i) to show that a simple polytopic model can be used for designing robust controllers for predominately inductive grids; (ii) to help in the choice of the control design parameter, based on a trade-off between an upper bound of the transient settling times and the control gain sizes. Linear matrix inequality based conditions are used to design the robust control gains with lower numerical complexity than similar conditions on literature. It is shown that small values the radius of pole location lead to better bounds for the transient responses, at the price of higher control gains. Good tracking of references for the grid currents is also illustrated in practice, allowing the closed-loop system to inject active and reactive power into the grid. Simulation and experimental results prove that the system connected to the grid can provide three-phase currents complying with requirements of an important international standard.     

New stability conditions via reflection coefficients of polynomials

The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Starting from so-called barycentric simplex some necessary stability conditions in terms of unions of polytopes are obtained by splitting the unit hypercube of reflection coefficients. Sufficient stability conditions in terms of linear covers of reflection vectors of a family of stable polynomials improve the Cohn stability criterion.     

Pole assignment for uncertain systems in a specified disk by output feedback

In this paper the problem of pole assignment in a disk by output feedback for continuous-or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given.     

Robust pole assignment for incomplete nonlinear decoupling applied to robots

A robustness analysis and synthesis for incomplete nonlinear decoupling for a class of nonlinear systems is discussed. Rigid and elastic-joint robot models belong to this class. For the elastic case, a transformation facilitates the robustness analysis under a weak assumption. Charts with H ₁- and H - norms of closed-loop disturbance transfer functions of the nonlinear-decoupled system are presented for a robust pole assignment.     

A continuation approach to eigenvalue assignment

This paper describes a continuation approach to eigenvalue assignment. The method is a homotopy technique which embeds the control problem into a parameterized family of control problems. This parameterization describes a continuous deformation of a system with the desired spectrum into the original system. Based on this deformation, a differential equation is constructed whose solution trajectory has an end-point which is a constant output feedback matrix assigning the desired spectrum to the original system. The derivation of this differential equation and conditions which guarantee the existence of a solution are given. Also, two examples of its numerical implementation are detailed.     

参数不确定性广义周期时变系统的鲁棒稳定性分析

基于广义周期时变系统允许的充分必要条件,提出了参数不确定性广义周期时交系统鲁棒稳定的概念,并得到了该类系统鲁棒稳定的充分必要条件．研究在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法．引入广义周期时变系统二次稳定的概念,讨论了二次稳定性与鲁棒稳定性的关系．最后通过数值算例说明了所得的主要结果,     

On pole assignment of linear systems by gain output feedback

In this paper, the Geometric Approach is used to derive in a straightforward way a sufficient condition for pole assignability by gain output feedback. This result leads to a pole assignment procedure which reduces to solving a system of min (n - m, n - p) polynomial equations where n is the number of states, m the number of inputs, p the number of outputs. In the case where m + p > n, this system clearly appears to be linear. The degrees of freedom related to the pole assignment problem are expressed in terms of (right or left) eigenvectors.     

Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals

This paper considers the problem of robust stability and robust stabilization for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent quadratic stability results, demonstrate that it allows the use of parameter-dependent Lyapunov functionals, and develop control design methods based on linear matrix inequalities (LMIs) for solving the robust control problem. Next, the problem of determining the maximum time-delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, illustrative examples are given to demonstrate the advantage of these new representations.