Lyapunov-Equation-Based Stability Analysis for Switched Linear Systems and Its Application to Switched Adaptive Control

This article investigates the stability of continuous-time switched linear systems with dwell-time constraints. A fresh insight into this established problem is provided via novel stability conditions that require the solution to a family of differential Lyapunov equations and algebraic Lyapunov equations. The proposed analysis, which leads...

Adaptive stabilization of impulsive switched linear time-delay systems: A piecewise dynamic gain approach

In the presence of discontinuous time-varying delays, neither Krasovskii nor Razumikhin techniques can be successfully applied to adaptive stabilization of uncertain switched time-delay systems. This paper develops a new adaptive control scheme for switched time-delay systems that can handle impulsive behavior in both states and time-varying...

Robust adaptive tracking control of uncertain slowly switched linear systems

In this paper, robust adaptive tracking control schemes for uncertain switched linear systems subject to disturbances are investigated. The robust adaptive control problem requires the design of both adaptive and switching laws. A novel adaptive law is proposed based on an extended leakage approach, which does not require knowledge of the bounds...

Reachable set estimation for switched linear systems with dwell-time switching

In this work we address the problem of (outer) estimation of reachable sets in switched linear systems subject to dwell-time switching. After giving some conditions that exploit the well-known properties of exponential decrease/bounded increase of the Lyapunov function (i.e. exponential decrease in between switching times and bounded increase...

A novel Lyapunov function for a non-weighted L₂ gain of asynchronously switched linear systems

In this paper, a novel Lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes. The novelty consists in continuity of the Lyapunov function at the switching instants and discontinuity when the system modes and controller modes are...

Online policy iterations for optimal control of input-saturated systems

This work proposes an online policy iteration procedure for the synthesis of sub-optimal control laws for uncertain Linear Time Invariant (LTI) Asymptotically Null-Controllable with Bounded Inputs (ANCBI) systems. The proposed policy iteration method relies on: a policy evaluation step with a piecewise quadratic Lyapunov function in both the...