Abstract
This paper is concerned with the finite time annular domain robust stability (FTADRS) analysis and controller design for T-S fuzzy positive systems with interval uncertainties. The concept of finite time annular domain stability is first introduced for positive systems. Based on this and using the copositive Lyapunov function approach, some sufficient conditions for FTADRS are derived. Subsequently, the finite time annular domain robust controller is designed via the linear programming technique. Finally, two numerical examples and an application example are employed to show the effectiveness of our results.
Highlights
Positive systems, whose states always remain in the nonnega- sugar levels within a safe range(i.e., 70-180 mg/dL) [18], tive orthant if its initial states and inputs are nonnegative, find [19]
Unlike the traditional finite time stability (FTS), the lower bound of issues were considered in [8]–[10], and the filtering problem 38 system states is constrained to a specific level in the defwas addressed in [11], [12]
Most of positive bound, which often leads to difficulty in FTADS analysis and systems possess more or less some nonlinear characteristics. control synthesis
Summary
Positive systems, whose states always remain in the nonnega- sugar levels within a safe range(i.e., 70-180 mg/dL) [18], tive orthant if its initial states and inputs are nonnegative, find [19]. Developing new methods on the FTADS analysis and control synthesis of nonlinear positive uncertain systems is 118 where x(t) ∈ Rn is the state of the system; u(t) ∈ Rs is the imperative, which motivates us to conduct this work. Numerous successful applications of T-S fuzzy model-based where Ai, Bi and Ai, Bi are the upper and lower bound matrices of Ai, Bi. By fuzzy blending, we can obtain the following overall T-S fuzzy model: methodology motivate us to employ the T-S model as a r vehicle to analyze the FTADS of nonlinear positive systems. Compared with the traditional FTS definition of positive systems in [15], the lower bound of system states is fully Lemma 2. Considering (14)-(16), we have g(t) ≥ aebt, ∀t ∈ [0, T ]
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