## What is/are Strict Lyapunov?

Strict Lyapunov - In this note, we use the Mazenc construction to design a simple strict Lyapunov function in a rather intuitive manner, based on a first-choice function whose derivative is negative semidefinite.^{[1]}In the stability analysis, a strict Lyapunov function and its conditions are studied to prove asymptotic stability for second-order systems and Lagrangian systems.

^{[2]}Two illustrative examples illustrate that the proposed scheme can be used to ensure UGES even though finding a common quadratic strict Lyapunov function is sometimes impossible for arbitrarily switched LTI systems.

^{[3]}The finite-time stability of the closed-loop attitude control system is proved by using a continuously-differentiable, homogeneous and strict Lyapunov function.

^{[4]}First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given.

^{[5]}Using the strict Lyapunov function, some sufficient conditions in terms of matrix inequalities are obtained for the boundary ISS of the closed-loop hyperbolic PDE-ODE systems.

^{[6]}Strict Lyapunov functions for these systems are provided.

^{[7]}Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented.

^{[8]}For a linear parameterization of the unknown parameters, a new strict Lyapunov function construction method is first presented for I&I adaptive control systems using the notion of integral inputto-state stability (iISS).

^{[9]}More significantly, for the first time in the literature, a strict Lyapunov function is provided and uniform global asymptotic stability for the closed-loop system is established.

^{[10]}For this new architecture we first prove a stability and performance analysis test, based on certain strict Lyapunov conditions, and show that these reduce to LMIs when using quadratic Lyapunov certificates.

^{[11]}For a realistic structure preserving power system with voltage dependent loads, we propose a sufficient condition based on a strict Lyapunov energy function, which is utilized to design a nonlinear adaptive SVC controller.

^{[12]}This paper proposes strict Lyapunov functions (SLFs) for the Saturated-Proportional-Saturated-Derivative with gravity cancellation controller for the case when the robot manipulator has non-ideal actuators and without taking into account the viscous friction in the model.

^{[13]}When a nonlinear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory.

^{[14]}Asymptotic stability of the closed loop system is proven using a Strict Lyapunov Function.

^{[15]}

## strict lyapunov function

In this note, we use the Mazenc construction to design a simple strict Lyapunov function in a rather intuitive manner, based on a first-choice function whose derivative is negative semidefinite.^{[1]}In the stability analysis, a strict Lyapunov function and its conditions are studied to prove asymptotic stability for second-order systems and Lagrangian systems.

^{[2]}Two illustrative examples illustrate that the proposed scheme can be used to ensure UGES even though finding a common quadratic strict Lyapunov function is sometimes impossible for arbitrarily switched LTI systems.

^{[3]}The finite-time stability of the closed-loop attitude control system is proved by using a continuously-differentiable, homogeneous and strict Lyapunov function.

^{[4]}First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given.

^{[5]}Using the strict Lyapunov function, some sufficient conditions in terms of matrix inequalities are obtained for the boundary ISS of the closed-loop hyperbolic PDE-ODE systems.

^{[6]}Strict Lyapunov functions for these systems are provided.

^{[7]}For a linear parameterization of the unknown parameters, a new strict Lyapunov function construction method is first presented for I&I adaptive control systems using the notion of integral inputto-state stability (iISS).

^{[8]}More significantly, for the first time in the literature, a strict Lyapunov function is provided and uniform global asymptotic stability for the closed-loop system is established.

^{[9]}This paper proposes strict Lyapunov functions (SLFs) for the Saturated-Proportional-Saturated-Derivative with gravity cancellation controller for the case when the robot manipulator has non-ideal actuators and without taking into account the viscous friction in the model.

^{[10]}When a nonlinear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory.

^{[11]}Asymptotic stability of the closed loop system is proven using a Strict Lyapunov Function.

^{[12]}