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Partial state estimation of LTI systems with multiple constant time-delays. (English) Zbl 1395.93127

Summary: Functional observer design for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 – delay-dependent, and 2 – internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of linear matrix inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen’s inequality, and improved Park’s inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

MSC:

93B07 Observability
93B15 Realizations from input-output data
93C05 Linear systems in control theory
93C23 Control/observation systems governed by functional-differential equations
93B51 Design techniques (robust design, computer-aided design, etc.)
93D20 Asymptotic stability in control theory
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