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Solution formulae are explicitly presented with the exposure of a relationship between the solutions to the three discrete-time, algebraic Riccati equations (DARE) required in the construction of an LSDP controller.
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Formulas (2)–(4) are iterated to obtain the optimal solution formula (1).
In Section 2 we derive the solution formula of our semi-linear problem.
Firstly, we derive the solution formula for the problem (1.1), (1.2).
The aim of this subsection is to derive the solution formula for the problem (1.1), (1.2).
The aim of this section is to derive the solution formula for the problem (1.1), (1.2).
To state our solution formulas of problem: (2.2 - 2.3 2.2 - 2.3oduce some classes of multipliers.
It adopts the scheme of cylindrical decomposition that consists of four phases projection, isolation, lifting, and solution formula construction.
In Section 2, we study the decay property of the solution operators appearing in the solution formula.
The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem:, , ,,.
We study the decay property of the solution operators appearing in the solution formula in Section 3.
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