Constrained pole placement for linear systems using low-order output feedback controllers

The paper presents a simple approach to the problem of designing low-order output feedback controllers for linear continuous systems. The controller can place all of the closed-loop poles within a circle, C(- , 1/ β) , with centre at - and radius of 1/ β in the left half s-plane. The design method is based on transformation of the original system and then applying the bounded-real-lemma to the transformed system. It is shown that subjected to the solvability of an algebraic Riccati equation (ARE), output feedback controllers can then be systematically derived. Furthermore, the order of the controller is low and equals only the number of the open-loop poles lying outside the circle. A step-by-step design algorithm is given. Numerical examples are given to illustrate the design method.

Design of reduced-order functional observers for linear systems with unknown inputs

This brief paper presents new conditions for the existence and design of reduced-order linear functional state observers for linear systems with unknown inputs. Systematic procedures for the synthesis of reduced-order functional observers are given. Numerical examples are given to illustrate the attractiveness and simplicity of the new design procedures.

Design of a common observer for two linear systems with unknown inputs

This paper considers the design of a common linear functional observer for two linear time-invariant systems with unknown inputs. A structure for a common observer which only uses the available output information is proposed. Here, for the proposed structure, we show that the simultaneous functional observation problem of two plants is reduced to a problem of designing two observers: the first is a full-order unknown input observer of one of the two systems; the second observer is a common unknown input observer of a system comprises two-connected systems. In general, the existence conditions for the second observer are very difficult to satisfy. This paper thus concludes that it is indeed very difficult to find a common observer for two linear systems with unknown inputs.

On the existence and design of functional observers for linear systems

Darouach [1] recently derived necessary and sufficient conditions for the existence and stability of functional observers with an order, p, equals to the dimension m of the vectors to be estimated. In general, these conditions are difficult to satisfy and when they are not, the only available option is to increase the order of the functional observers. This note presents new conditions for the existence of a general pth-order functional observer. Systematic procedures for the synthesis of reduced-order functional observers are given. A numerical example is given to illustrate the design procedures.

A common disturbance decoupled observer for linear systems with unknown inputs

This paper presents a solution to the problem of designing a common linear functional observer that can observe a partial set of the state vector of two linear systems with unknown inputs. A new structure of a decoupled linear functional observer is proposed for systems subject unknown disturbances, using only the available output information. Existence conditions as well as a design procedure are given for constructing the proposed observer. A numerical example is given to illustrate the effectiveness of the new observer structure.