Document Type : Original Research Paper
Authors
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran
Abstract
This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity property of the optimal state trajectory of the closed-loop system is also guaranteed. Furthermore, state variables of the closed-loop system converge to the origin in finite steps (finite-time stability). In this regard, the LQR+(positive LQR) problem for the linear discrete time systems is stated. Once, the cost function with finite-time horizon is considered and another time the cost function with infinite-time horizon is assumed. In this regard, two theorems are given and proved which consider the problem of building positive and also optimize of the linear time-varying discrete time systems. Results can also be applied to linear time-invariant discrete time systems. Finally, computer simulations are given to illustrate effective performance of the designed controller and also verify the theoretical results.
Keywords
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