Stability robustness analysis of state-space models for uncertain Linear time-varying systems

Stability Analysis for Linear Time-Varying Systems With Uncertain Parameters: Application to Steady-State Solutions of Nonlinear Systems

“…To demonstrate this, it is shown below that the stability bound (17) obtained here is always less than or equal to one of the bounds proposed by Xi (1994), where 6max ( . ) denotes the maximum singular value, see Definition 1 in Xi (1994), and Here, P(t) is the positive defmite solution of equation ( 7) for Q(t) = 2I. Thus, AQ = 2, PI (t) = PT (t) + P, (t) and umax (P, (t)) :5 2Gmax(P,(t)).…”

“…From this inequality, it can be seen that the stability bound on one parameter is dependent on the size of the uncertainties in other parameters. The significance of this theorem is that it takes into consideration the directional information that is often available in practical applications, thus reducing the conservatism found in previous results given by Xi (1994). To demonstrate this, it is shown below that the stability bound (17) obtained here is always less than or equal to one of the bounds proposed by Xi (1994), where 6max ( . )…”

“…The significance of this theorem is that it takes into consideration the directional information that is often available in practical applications, thus reducing the conservatism found in previous results given by Xi (1994). To demonstrate this, it is shown below that the stability bound (17) obtained here is always less than or equal to one of the bounds proposed by Xi (1994), where 6max ( . ) denotes the maximum singular value, see Definition 1 in Xi (1994), and Here, P(t) is the positive defmite solution of equation ( 7) for Q(t) = 2I.…”

“…It is difficult to get stability bounds for these by using the above stability robustness measurements. Recently, Xi (1994) derived stability bounds on parameter uncertainties for a time-varying system. The results are restricted to bounds on the absolute values of the uncertain parameters; that is, the corresponding stable region in parameter space is always symmetric with respect to the origin.…”

“…The Lyapunov approach is employed to obtain bounds on the uncertain time-varying parameters to guarantee the stability. The robust stability bounds obtained are not necessarily symmetric with respect to the origin in the parameter space and can significantly reduce the conservatism in the previous results (Xi, 1994). The results developed are applied to investigate the stability of the steady-state responses of nonlinear systems (especially of piecewise linear systems) subjected to periodic excitations.…”