Abstract
This paper deals with the finite-time interval observer design method for discrete-time switched systems subjected to disturbances. The disturbances of the system are unknown but bounded. The framework of the finite-time interval observer is established and the sufficient conditions are derived by the multiple linear copositive Lyapunov function. Furthermore, the conditions which are expressed by the forms of linear programming are numerically tractable by standard computing software. One example is simulated to illustrate the validity of the designed observer.
Highlights
State estimation is very important since it can be used in stabilization, synchronization, fault diagnosis and detection and so on
It is desired that A À LC is both non-negative and Schur stable
Whereas it only requires that A À LC is Schur stable in the context of conventional observers
Summary
State estimation is very important since it can be used in stabilization, synchronization, fault diagnosis and detection and so on. Keywords Finite-time interval observers, discrete-time switched systems, linear programming If we consider a linear discrete system without disturbance, that is, x(k + 1) = Ax(k) + Bu(k), the task of IO design is to find a gain L such that the corresponding upper (or lower) error system e+(À)(k + 1) = (A À LC)e+(À)(k) is both positive and stable. In order to improve the former results, Guo and Zhu21 and Ethabet et al.22 presented the IO design approaches for uncertain discrete-time and continuous-time switched systems using coordinate transformation, respectively.
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