Practical stability analysis and switching controller synthesis for discrete-time switched affine systems via linear matrix inequalities

This paper considers the practical asymptotic stabilization of a desired equilibrium point in discrete-time switched affine systems. The main purpose is to design a state feedback switching rule for the discrete-time switched affine systems whose parameters can be extracted with less computational complexities. Tn this regard, using switched Lyapunov functions, a new set of sufficient conditions based on matrix inequalities, are developed to solve the practical stabilization problem. For any size of the switched affine system, the derived matrix inequalities contain only one bilinear term as a multiplication of a positive scalar and a positive definite matrix. Tt is shown that the practical stabilization problem can be solved via a few convex optimization problems, including Linear Matrix Tnequalities (LMTs) through gridding of a scalar variable interval between zero and one. The numerical experiments on an academic example and a DC-DC buck-boost converter, as well as comparative studies with the existing works, prove the satisfactory operation of the proposed method in achieving better performances and more tractable numerical solutions. (c) 2024 Sharif University of Technology. All rights reserved.