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2 International Journal of Applied Mathematics and Computer Science

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A unified convex combination approach to switched uncertain nonlinear systems

Chang Yufang, Zhai Guisheng, Fu Bo

International Journal of Applied Mathematics and Computer Science

2025

Vol. 35, no. 1

117--128

We address a unified convex combination approach to a class of switched uncertain nonlinear systems, focusing on quadratic stability and L2 gain. In each subsystem, there are norm-bounded uncertainties in the system matrix and nonlinear terms with quadratic constraints. The proposed convex combination is original and unified in the sense of incorporating not only the nominal subsystem matrices but also uncertainty and quadratic constraints in the same form. When there is no single subsystem having the desired performance but a convex combination of subsystems does, we design a switching law so that the switched system achieves the same performance. Moreover, the discussion is extended to switching state feedback and its application to a boost converter.

Decentralized static output feedback controller design for linear interconnected systems

Fadhilah Helisyah Nur, Adzkiya Dieky, Arif Didik Khusnul, Zhai Guisheng, Mardlijah

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 1

83--96

Many interconnected systems in the real world, such as power systems and chemical processes, are often composed of subsystems. A decentralized controller is suitable for an interconnected system because of its more practical and accessible implementation. We use the homotopy method to compute a decentralized controller. Since the centralized controller constitutes the starting point for the method, its existence becomes very important. This paper introduces a non-singular matrix and a design parameter to generate a centralized controller. If the initial centralized controller fails, we can change the value of the design parameter to generate a new centralized controller. A sufficient condition for a decentralized controller is given as a bilinear matrix inequality with three matrix variables: a controller gain matrix and a pair of other matrix variables. Finally, we present numerical examples to validate the proposed decentralized controller design method.