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We propose a construction of Lyapunov functions for linear and bilinear infinite-dimensional integral input-to-state stable systems. In contrast to other constructions available in the literature, we do not impose strong restrictions on the type of the bilinear systems. The coercivity of such Lyapunov functions as well as a possible extension to systems with unbounded input operators are discussed.
New sufficient conditions for the robust stability of continuous-time linear systems with the norm-bounded additive/ multiplicative uncertainty are proposed. These criteria are based on the feasibility test of a set of linear matrix inequalities (LMIs) obtained from homogeneous polynomial Lyapunov functions (HPLFs). It is shown that these proposed criteria are less conservative than those obtained...
In this paper we study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be ldquouniversalrdquo for the uncertain system under consideration if the search of a Lyapunov function that proves the robust stability of the system...
This paper focuses on the problem of robust stabilization for differential or discrete linear repetitive processes. The provided conditions allow us to involve parameter dependent Lyapunov functions. An additional flexibility in finding a solution is obtained by introducing slack matrix variables. A simulation example is given to illustrate the theoretical developments.
This paper discusses linear fractional representations (LFR) of parameter-dependent nonlinear systems with real-rational nonlinearities and point-delayed dynamics. Sufficient conditions for robust global asymptotic stability both independent of and dependent on the delays are investigated via linear matrix inequalities. Such inequalities are obtained from the values of the time-derivatives of appropriate...
Stability of linear impulsive control system is investigated in this thesis, and then a method with impulsive control to assign the eigenvalues of a time-invariant linear system is discussed. Based on the proper Lyapunov functions and the Riccati linear inequality, some sufficient conditions are presented in this paper for impulsive control system with mixing perturbation. Also, some remarks and an...
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