Stability analysis of 2‐D discrete and continuous state‐space systems

Abstract

Abstract This paper presents new stability conditions for two‐dimensional (2‐D) systems in state‐space description. Both discrete and continuous systems are studied. These results are based on the criteria first presented by Huang, De Carlo, Strintzis, Murray, Delsarte, et al. and on the discrete Lyapunov equation with complex elements for 2‐D systems. The stability properties of the Mansour matrix are also used for stability testing in state‐space. Criteria for the VSHP property of 2‐D polynomials are further presented using the continuous Lyapunov equation with complex elements and the stability properties of the Schwarz matrix form. The stability properties of the Schwarz matrix are also used for testing the VSHP property of 2‐D polynomials in state‐space. The proposed new criteria are non‐conservative for the stability analysis of 2‐D discrete and continuous systems and achieve the aim of reducing the original 2‐D problem as much as possible to a set of 1‐D stability tests. Numerical examples are given to illustrate the utility of the proposed conditions.