Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

Abstract

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. In 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. It is shown that the practical stabilization problem can be solved via a few convex optimization problems, including Linear Matrix Inequalities (LMIs) 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.

Design of a Switching Strategy for Output Voltage Tracking Control in a DC-DC Buck Power Converter

“…A robust state-feedback switching law for the switched system utilizing the sliding mode theory was developed in [14] to ensure the robust asymptotic stability of the desired equilibrium point for the Buck converter. While Hejri, in [15], using switched Lyapunov functions, a set of sufficient conditions based on matrix inequalities, reduced the computational complexity and solved the stabilization problem for the DC/DC converter, de Souza et al in [16] developed a strategy to limit the switching frequency using a state-dependent switching law for switched systems for stabilization at the desired equilibrium. Another switching strategy consists of an adaptive sliding mode control that combines a robust proportional-derivative control law for the regulation of the DC/DC Buck converter-DC motor system presented in [17].…”

“…Motivated by the benefits of a commutated control strategy [12][13][14][15][16][17][18][19], the design of a suitable switching function by means of the application of convex sets for the output trajectory tracking of a Buck power electronic converter is presented here. Unlike in [12][13][14][15][16][17][18][19], this control resolves voltage tracking at the converter load.…”

“…Motivated by the benefits of a commutated control strategy [12][13][14][15][16][17][18][19], the design of a suitable switching function by means of the application of convex sets for the output trajectory tracking of a Buck power electronic converter is presented here. Unlike in [12][13][14][15][16][17][18][19], this control resolves voltage tracking at the converter load. The use of convex sets in the commutated control strategy presented here allows for resolving the tracking for different desired voltage trajectories for the Buck converter in milliseconds, even in the presence of abrupt disturbances in the load and source.…”