01886nas a2200145 4500008004100000245010700041210006900148300001300217490000700230520132500237653001301562100001601575700001101591856013801602 2008 eng d00aUniform Semiglobal Practical Asymptotic Stability for Non-autonomous Cascaded Systems and Applications0 aUniform Semiglobal Practical Asymptotic Stability for Nonautonom a337-347 0 v443 a

It is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when \emph{decoupled}, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, ıt e.g.}, in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, ıt etc}. After giving a rigorous framework for the analysis of such stability properties, this paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition on its solutions, the cascade of two USPAS systems remains USPAS. An analogous result is derived for uniformly semiglobally asymptotically stable (USAS) systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems affected by unknown non-dissipative forces and considering the dynamics of the DC motors.

10aRobotics1 aChaillet, A1 aLor, A uhttps://www.centropiaggio.unipi.it/publications/uniform-semiglobal-practical-asymptotic-stability-non-autonomous-cascaded-systems-and01255nas a2200145 4500008004100000245013000041210006900171520065700240653001300897100001600910700001500926700001100941700001700952856014000969 2007 eng d00aUniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases0 aUniform stabilization for linear systems with persistency of exc3 a

Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting. In particular, when $\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback, only depending on $(A,B)$ and the parameters of the persistent excitation, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when $A$ is neutrally stable and when the system is the double integrator.

10aRobotics1 aChaillet, A1 aChitour, Y1 aLor, A1 aSigalotti, M uhttps://www.centropiaggio.unipi.it/publications/uniform-stabilization-linear-systems-persistency-excitation-neutrally-stable-and-double00948nas a2200133 4500008004100000245008600041210006900127490000700196520043600203653001300639100001600652700001100668856013500679 2006 eng d00aUniform global practical asymptotic stability for non-autonomous cascaded systems0 aUniform global practical asymptotic stability for nonautonomous 0 v123 a

This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalise previous theorems that establish the uniform global asymptotic stability of cascades.

10aRobotics1 aChaillet, A1 aLor, A uhttps://www.centropiaggio.unipi.it/publications/uniform-global-practical-asymptotic-stability-non-autonomous-cascaded-systems.html00942nas a2200133 4500008004100000245007500041210006900116260002300185520043600208653001300644100001600657700001100673856012400684 2006 eng d00aUniform Global Practical Stability for non-autonomous cascaded systems0 aUniform Global Practical Stability for nonautonomous cascaded sy aKyoto, JapancJuly3 a

This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalize previous theorems that establish the uniform global asymptotic stability of cascades.

10aRobotics1 aChaillet, A1 aLor, A uhttps://www.centropiaggio.unipi.it/publications/uniform-global-practical-stability-non-autonomous-cascaded-systems.html00538nas a2200121 4500008004100000245010000041210006900141260003300210653001300243100001600256700001100272856013300283 2005 eng d00aUniform Semiglobal Practical Asymptotic Stability for nonlinear time-varying systems in cascade0 aUniform Semiglobal Practical Asymptotic Stability for nonlinear  aPraha, Tcheck RepubliccJuly10aRobotics1 aChaillet, A1 aLor, A uhttps://www.centropiaggio.unipi.it/publications/uniform-semiglobal-practical-asymptotic-stability-nonlinear-time-varying-systems