765 research outputs found
Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications
It is due to the modularity of the analysis 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 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, e.g., in control of physical systems with
external perturbations, measurement noise, unmodelled dynamics, etc. This paper
generalizes previous results for cascades by establishing that, under a uniform
boundedness condition, the cascade of two USPAS systems remains USPAS. An
analogous result can be derived for USAS systems in cascade. Furthermore, we
show the utility of our results in the PID control of mechanical systems
considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that
links the parameter-dependency of the lower and upper bounds on the Lyapunov
function, stronger condition of uniform boundedness of solutions,
modification and simplification of the proofs accordingl
3 sampled-data control of nonlinear systems
This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research
On the robustness analysis of triangular nonlinear systems: iISS and practical stability
International audienceThis note synthesizes recent results obtained by the authors on the stability and robustness analysis of cascaded systems. It focuses on two properties of interest when dealing with perturbed systems, namely integral input-to-state stability and practical stability. We present sufficient conditions for which each of these notions is preserved under cascade interconnection. The obtained conditions are of a structural nature, which makes their use particularly easy in practice
Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems
We provide explicit closed form expressions for strict Lyapunov functions for
time-varying discrete time systems. Our Lyapunov functions are expressed in
terms of known nonstrict Lyapunov functions for the dynamics and finite sums of
persistency of excitation parameters. This provides a discrete time analog of
our previous continuous time Lyapunov function constructions. We also construct
explicit strict Lyapunov functions for systems satisfying nonstrict discrete
time analogs of the conditions from Matrosov's Theorem. We use our methods to
build strict Lyapunov functions for time-varying hybrid systems that contain
mixtures of continuous and discrete time evolutions.Comment: 14 pages. Accepted for publication in Nonlinear Analysis: Hybrid
Systems and Applications on September 6, 200
Nested ocean models: Work in progress
The ongoing work of combining three existing software programs into a nested grid oceanography model is detailed. The HYPER domain decomposition program, the SPEM ocean modeling program, and a quasi-geostrophic model written in England are being combined into a general ocean modeling facility. This facility will be used to test the viability and the capability of two-way nested grids in the North Atlantic
RAINIER: A Simulation Tool for Distributions of Excited Nuclear States and Cascade Fluctuations
A new code has been developed named RAINIER that simulates the -ray
decay of discrete and quasi-continuum nuclear levels for a user-specified range
of energy, angular momentum, and parity including a realistic treatment of
level spacing and transition width fluctuations. A similar program, DICEBOX,
uses the Monte Carlo method to simulate level and width fluctuations but is
restricted to -ray decay from no more than two initial states such as
de-excitation following thermal neutron capture. On the other hand, modern
reaction codes such as TALYS and EMPIRE populate a wide range of states in the
residual nucleus prior to -ray decay, but do not go beyond the use of
deterministic functions and therefore neglect cascade fluctuations. This
combination of capabilities allows RAINIER to be used to determine
quasi-continuum properties through comparison with experimental data. Several
examples are given that demonstrate how cascade fluctuations influence
experimental high-resolution -ray spectra from reactions that populate
a wide range of initial states.Comment: 14 pages, 13 figures, Nuclear Instrumentation and Methods A, 201
Sampled-data steering of unicycles via PBC
In this paper, on the basis of a recently proposed discrete-time port-Hamiltonian representation of sampled-data dynamics, we propose a new time-varying digital feedback for steering mobile robots. The quality of the proposed passivity-based control is validated and compared through simulations with the existing literature and the continuous-time implementation using the unicycle as a case study
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