Upper bounds on trajectory deviations for an affine family of discrete-time systems under exogenous disturbances

We propose a simple upper bound on trajectory deviations for an affine family of discrete-time systems under nonzero initial conditions subjected to bounded exogenous disturbances. It involves the design of a parametric quadratic Lyapunov function for the system. The apparatus of linear matrix inequalities and the method of invariant ellipsoids are used as technical tools. The original problem is reduced to a parametric semidefinite programming problem, which is easily solved numerically. Numerical simulation results demonstrate the relatively low conservatism of the upper bound. This paper continues the series of our previous publications on estimating trajectory deviations for linear continuous- and discrete-time systems with parametric uncertainty and exogenous disturbances. The results presented below can be extended to various robust formulations of the original problem and also the problem of minimizing trajectory deviations for an affine family of discrete-time control systems under exogenous disturbances via linear feedback.