aDepartment of Electrical and Computer Engineering, Polytechnic University, Six Metrotech Center, Brooklyn, NY 11201, USA
bDepartment of Mathematical Sciences,Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA
Abstract:
We derive in this work a local nonlinear small-gain theorem in the framework of input-to-state stability for discrete time systems. Our primary objective is to show that, as in the continuous-time context, these discrete-time nonlinear small-gain theorems are very effective in stability analysis and synthesis for various classes of discrete-time control systems. Two converse Lyapunov theorems for discrete exponential stability are developed to assist these applications. New results in stability and stabilization presented in this paper are significant extensions of previous work by other authors (IEEE Trans. Automat. Control 38 (1993) 1398; 39 (1994) 2340; 33 (1988) 1082).