http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/0593.pdf

Brief paper: A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems

A Parametric Lyapunov Equation Approach to Low Gain Feedback Design for Discrete-time Systems

This study is concerned with designing a feedback gain to minimise a quadratic performance index with guaranteed pole locations for closed-loop discrete-time linear systems. Firstly, a method that shifts the open-loop poles to desired locations by using a parametric linear Stein equation is presented. Then a recursive approach is proposed to shift every eigenvalue of a discrete-time linear system separately without mode decomposition in each step. By using such method, it is required to solve a linear Stein matrix equation of low order in each step. The presented method yields a solution which is optimal with respect to a quadratic performance index that can be obtained explicitly. The attractive feature of this method comparing with existing results is that it enables solutions to complex problems to be easily found without solving any non-linear algebraic Riccati equations. Moreover, analytical solutions can be obtained which may have advantages in some design problems. Numerical examples illustrate the proposed approach.

Optimal pole assignment for discrete-time systems via Stein equations

In this paper, a method of pole assignment in H ∞ control theory is proposed. By this method, all the poles can be placed in a left half-plane or inside a disc on the complex plane and at the same time an H ∞ norm constraint is satisfied. This result can be derived by a bilinear transformation of the complex variable of a transfer function in H ∞ control theory

H∞ control with pole assignment in a specified disc

This paper deals with the stabilization problem for discrete-time linear system with unsymmetric saturation. To handle the structural properties of the unsymmetric saturation nonlinearity, the description of the transformation carries from the symmetric case to the unsymmetric case is employed. By using the parametric Lyapunov equation-based low gain feedback design approach, linear matrix inequality formulations for the state feedback and output feedback control design are given. The effectiveness of the proposed method is confirmed by numerical examples.

Semi-global stabilization of discrete-time linear systems with unsymmetrical saturation.

This paper is concerned with a property of a certain transformation of a matrix in terms of eigenvalues. The transformation, which results in a circle-symmetric shifting of eigenvalues, is derived by using a solution of an algebraic Riccati equation. A concept of the circle-symmetry is introduced.

On a shift of eigenvalues of a matrix by using a solution of an algebraic Riccati equation

https://www.jstage.jst.go.jp/article/sicetr1965/16/2/16_2_147/_pdf

A Design Method for a Feedback Control Law to Locate the Eigenvalues in a Specified Region in Linear Discrete-Time Systems

This paper deals with a method of synthesizing optimal control for a class of multivariable linear stochastic discrete-time systems with parameter variations. As is well known, for this type of control problem, the“self-tuning regulator”is proposed. The regulator recursively identifies and corrects the model, which is used to derive the control law, until the model matches the controlled object. The selftuning regulator becomes effective, however, only when the parameters of the controlled object are unknown constants or very slow variables. In the other case, namely, when a variable which represents the cause of parameter variations varies around its nominal value, the concept of sensitivities seems to be applicable. In this paper, the closed-loop control law which minimizes a quadratic performance index containing sensitivity variable is derived. The optimal control becomes a linear dynamical system. All the equations to be solved are linear, but there are equations having no unique solution. Therefore, it is shown that every solution yields the same control law, and any solution might as well be used to synthesize an optimal control system.

Yasuchika Mori

Papers

On a shift of eigenvalues of a matrix by using a solution of an algebraic Riccati equation

A Design Method for a Feedback Control Law to Locate the Eigenvalues in a Specified Region in Linear Discrete-Time Systems

A Synthesis Method for Low Sensitivity Closed-Loop Control System in Multivariable Linear Discrete-Time Systems

Suboptimal Control for Linear Discrete-Time System with Distributed-Delay by Considering Sensitivities