**Stabilizability Conditions for Switched Linear Systems**

with Constant Input via Switched Observer

with Constant Input via Switched Observer

**Takuya SOGA ^{1}, Naohisa OTSUKA^{2}**

^{1 }Graduate School of Advanced Science and Technology, Tokyo Denki University,

Hatoyama-Machi, Hiki-Gun, Saitama, 350-0394, Japan

^{2 }Division of Science, School of Science and Engineering, Tokyo Denki University,

Hatoyama-Machi, Hiki-Gun, Saitama, 350-0394, Japan

otsuka@mail.dendai.ac.jp

**Abstract**: In this paper, stabilizability conditions for switched linear systems with constant input via two types of switched rule which depends on the state of switched observer are presented. The obtained results provide stabilizability conditions via state feedback switched rule. Further, two illustrative numerical examples are also given.

**Keywords**: Switched Systems, Switched Observer, Stabilizability, Constant Input

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**CITE THIS PAPER AS**:

Takuya SOGA, Naohisa OTSUKA, **Stabilizability Conditions for Switched Linear Systems with Constant Input via Switched Observer**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 22 (1), pp. 7-14, 2013.

**Introduction**

Switched system is one of the so-called hybrid systems which consist of a family of subsystems and a switching rule among them. The aspect of the switched system is found in various fields such as aircraft industry, mobile robot, animal world and Ethernet etc[3], [7]. Further, the idea of switching has also been used to design intelligent control which is based on the switching between different controllers. An important problem in such switched systems is the stability problem with arbitrary switching and the stabilization problem via appropriate switching rule. Until now many results on stability and stabilization problems for various types of switched linear systems without input have been studied (e.g., [1],[2],[5], [6], [8]-[20]).

In addition, it is also important to consider the case which contains the control input for practical applications. In particular, Deaecto et al. [4] gave some conditions for some equilibrium point to be globally asymptotically stable via state feedback switched rule. The conditions are related to continuous-time switched linear system with constant input. The results were applied to DC-DC converters control design. However, the same problems via switched observer which contains information of the outputs instead of the state for the switched systems have not been investigated.

The objective of this paper is to study conditions under which equilibrium points are globally asymptotically stable via the switched observer. The conditions are related to continuous-time switched linear systems with constant input. In Section 2 the main results of this paper are given. In Section 3 two illustrative numerical examples are shown. Finally, concluding remarks are given in Section 4.

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