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The static output feedback (SOF) synthesis problem for descriptor systems is considered in this paper. LMI-based algorithms are proposed to find potentially structured SOF gains ensuring admissibility and even

The descriptor framework encompasses a wide class of systems [

The static output feedback (SOF) control problem plays a central role in control theory and applications (see, e.g., [

In this paper, a novel coordinate-descent iterative numerical procedure that can synthesize a SOF, ensuring the admissibility of the closed-loop system, is derived in the continuous time setting. The proposed algorithm does not require any special decomposition of the considered descriptor system. Contrary to some existing iterative LMI algorithms (see, e.g., [

Furthermore, it is well known in control theory that an important problem in control arises when a specific structure on the overall control scheme is considered, especially when dealing with complex or distributed systems. Thus, we extend the proposed algorithms to deal with SOF

In addition, the observer-based

This paper is organized as follows. some preliminary results on descriptor systems are recalled in Section

The notation

Let us consider the descriptor system given by

If

System (

As defined above, the admissibility of descriptor systems can be formulated as an LMI feasibility problem as stated in [

System (

For a given positive number

Let

In this section, the static output feedback (SOF) admissibility control for descriptor systems given by (

The SOF admissibility control problem is to find an SOF controller:

According to Lemma

Recall that the matrix

By setting:

Following the same lines as above, we can set:

However, equalities (

and fixing

Based on this, an iterative algorithm is proposed hereafter to find an initial pair

We have the following steps.

Set

Solve the following optimization problem for

If trace

If the difference of two iterations is small that is trace

Set

We have the following steps.

Set

Solve the following optimization problem for

Minimize

If

Set

If

Solve the following optimization problem for

Minimize

If

(i) To shed light on the role of the computation parameter

(ii) In Algorithm

(iii) The discussion on the iterative procedure and convergence, particularly, of Algorithm

(iv) As iterative LMI methods, when the proposed procedure fails to find a solution it does not mean that no solution can be found.

Consider the SOF admissibility control problem of system (

Consider the SOF admissibility control problem of (

In this section, the structured SOF admissibility control problem is investigated. The structure constraint on the SOF controller is defined by

It is easy to see that

The main idea underlying Algorithm

We have the following steps.

Set

Solve the following optimization problem for

If

Solve the following optimization problem for

If

Consider the structured SOF admissibility control problem of (

A structured SOF admissibility control problem.

Algorithm | Iterations number | The obtained SOF |
---|---|---|

Algorithms | 1+3 | |

Algorithm | 7 |

The objective of the SOF

We sum up briefly the construction of these algorithms in the following.

It is constructed by using the LMI constraints:

It is constructed by using the LMI constraints:

Consider the SOF

Following the same lines as in Algorithm

Consider the structured SOF

A structured SOF

Algorithm | Iterations number | The obtained SOF |
---|---|---|

Algorithms | 1+7 | |

6 | 2 |

In this section, an alternative technique for determining observer-based

Consider the descriptor system (

The closed-loop system is given by

Consider the observer-based

In this note, the static output feedback synthesis problem for descriptor systems is considered. Some LMI–based algorithms to find potentially structured SOF gains ensuring admissibility and